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It [The Turn of the Screw] is an excursion into chaos while remaining, like Blue-Beard and Cinderella, but an anecdote—though an anecdote amplified and highly emphasized and returning upon itself; as, for that matter, Cinderella and Blue-Beard return. I need scarcely add after this that it is a piece of ingenuity pure and simple, of cold artistic calculation, an amusette to catch those not easily caught (the “fun” of the capture of the merely witless being ever but small), the jaded, the disillusioned, the fastidious.
Felman's gloss of these appears to be that James is indicating here that the story is trying to "catch" sophisticated or intelligent readers in a trap of misreadings before illuminating them with a simple and obvious explanation:
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Nothing is so easy as improvisation, the running on and on of invention; it is sadly compromised, however, from the moment its stream breaks bounds and gets into flood. Then the waters may spread indeed, gathering houses and herds and crops and cities into their arms and wrenching off, for our amusement, the whole face of the land – only violating by the same stroke our sense of the course and the channel, which is our sense of the uses of a stream and the virtue of a story. Improvisation, as in the Arabian Nights, may keep on terms with encountered objects by sweeping them in and floating them on its breast; but the great effect it so loses – that of keeping on terms with itself. This is ever, I intimate, the hard thing for the fairy-tale; but by just so much as it struck me as hard did it in The turn of the screw affect me as irresistibly prescribed. To improvise with extreme freedom and yet at the same time without the possibility of ravage, without the hint of a flood; to keep the stream, in a word, on something like ideal terms with itself : that was here my definite business. The thing was to aim at absolute singleness, clearness and roundness, and yet to depend on an imagination working freely, working (call it) with extravagance; by which law it would n’t be thinkable except as free and would n’t be amusing except as controlled. The merit of the tale, as it stands, is accordingly, I judge, that it has struggled successfully with its dangers. It is an excursion into chaos while remaining, like Blue-Beard and Cinderella, but an anecdote – though an anecdote amplified and highly emphasised and returning upon itself ; as, for that matter, Cinderella and Blue-Beard return. I need scarcely add after this that it is a piece of ingenuity pure and simple, of cold artistic calculation, an amusette to catch those not easily caught (the ‘fun’ of the capture of the merely witless being ever but small), the jaded, the disillusioned, the fastidious. Otherwise expressed, the study is of a conceived ‘tone’, the tone of suspected and felt trouble, of an inordinate and incalculable sort – the tone of tragic, yet of exquisite, mystification. To knead the subject of my young friend’s, the supposititious narrator’s, mystification thick, and yet strain the expression of it so clear and fine that beauty would result: no side of the matter so revives for me as that endeavour. Indeed if the artistic value of such an experiment be measured by the intellectual echoes it may again, long after, set in motion, the case would make in favour of this little firm fantasy – which I seem to see draw behind it to-day a train of associations. I ought doubtless to blush for thus confessing them so numerous that I can but pick among them for reference. I recall for instance a reproach made me by a reader capable evidently, for the time, of some attention, but not quite capable of enough, who complained that I had n’t sufficiently ‘characterised’ my young woman engaged in her labyrinth; had n’t endowed her with signs and marks, features and humours, had n’t in a word invited her to deal with her own mystery as well as with that of Peter Quint, Miss Jessel and the hapless children. I remember well, whatever the absurdity of its now coming back to me, my reply to that criticism – under which one’s artistic, one’s ironic heart shook for the instant almost to breaking. “You indulge in that stricture at your ease, and I don’t mind confiding to you that – strange as it may appear! – one has to choose ever so delicately among one’s difficulties, attaching one’s self to the greatest, bearing hard on those and intelligently neglecting the others. If one attempts to tackle them all one is certain to deal completely with none; whereas the effectual dealing with a few casts a blest golden haze under cover of which, like wanton mocking goddesses in clouds, the others find prudent to retire. It was ‘déjà très-joli’, in The turn of the screw, please believe, the general proposition of our young woman’s keeping crystalline her record of so many intense anomalies and obscurities – by which I don’t of course mean her explanation of them, a different matter; and I saw no way, I feebly grant (fighting, at the best too, periodically, for every grudged inch of my space) to exhibit her in relations other than those; one of which, precisely, would have been her relation to her own nature. We have surely as much of her own nature as we can swallow in watching it reflect her anxieties and inductions. It constitutes no little of a character indeed, in such conditions, for a young person, as she says, ‘privately bred’, that she is able to make her particular credible statement of such strange matters. She has ‘authority’, which is a good deal to have given her, and I could n’t have arrived at so much had I clumsily tried for more.” [Bold added where Felman draws his quotation from]
The first few sentences lay out the paragraphs topic: how to keep improvisation within aesthetic boundaries. The image of the river shows the flowing nature of invention as well as it's tendency to get out of hand. James is saying that invention or improvisation can manage to depict things well enough, but it struggles to stay true to itself as a story and art. It needs some control to keep in bounds. James goes on to tell readers that he sees
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Improvisation, as in the Arabian Nights, may keep on terms with encountered objects by sweeping them in and floating them on its breast; but the great effect it so loses – that of keeping on terms with itself. This is ever, I intimate, the hard thing for the fairy-tale; but by just so much as it struck me as hard did it in The turn of the screw affect me as irresistibly prescribed. To improvise with extreme freedom and yet at the same time without the possibility of ravage, without the hint of a flood; to keep the stream, in a word, on something like ideal terms with itself
James concludes that he's done exactly that: "The merit of the tale, as it stands, is accordingly, I judge, that it has struggled successfully with its dangers." This is where Felman's quotation comes in:
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It is an excursion into chaos while remaining, like Blue-Beard and Cinderella, but an anecdote – though an anecdote amplified and highly emphasised and returning upon itself ; as, for that matter, Cinderella and Blue-Beard return. I need scarcely add after this that it is a piece of ingenuity pure and simple, of cold artistic calculation, an amusette to catch those not easily caught (the ‘fun’ of the capture of the merely witless being ever but small), the jaded, the disillusioned, the fastidious.
The first sentence just reinterates what's been said above. The story is an "excursion into chaos" like the river overflowing. Yet, it's a controlled "anecdote" that comes back to the rules that bind effective storytelling: it "return[s] upon itself." The paragraph is pretty much entirely about invention and storytelling. How does one improvise, but still keep the story interesting, entertaining, dramatic, well-formed? The next sentence phrases itself as just a further extension of this idea: "I need scarcely add after this that." So, we assume that it's going to go further into this idea of improvising, yet staying artistic: "it is a piece of ingenuity pure and simple, of cold artistic calculation, an amusette to catch those not easily caught (the ‘fun’ of the capture of the merely witless being ever but small), the jaded, the disillusioned, the fastidious." (An "amusette" is French for a frivolous pastime or diversion.) "Capture" in this context doesn't really sound like a trap here. What's being captured is not misreadings (those have never been talked about in the entire paragraph, nor will they be discussed in what follows). Rather, it sounds like interest. The concern of this paragraph (which this sentence is supposed to be an extension of--"I need scarcely add after this that") has been with the danger of improvisation turning ugly, uninteresting, and non-artistic. James is trying to sell his story as an improvised anecdote that's also aesthetic and interesting. That's what's being talked about here. After talking about improvisation for so long, he's trying to reassure readers that there's still a story to be had. And, it's a story that will "capture" readers--difficult readers. Readers disillusioned or fastidious are hard readers for a anecdote like a fairy tale to "capture." That's part of the exercise that James is doing here. Nowhere does this paragraph or even this sentence indicate that James is trying to create a misreading. Why would he jam that suggesting into a paragraph about improvising an interesting anecdote? Why would he jam it into a sentence that claims to be an extension of the thoughts in the paragraph? Why would he then return to talking about improvisation again immediately after talking about reading and misreading? 
