Not really sure how this latest American folly is on topic for the BA forum, to be totally frank. However, one thing I know for sure is that no one in the Airline community, at least in Europe, had prior notification of this “integrity fee”.
There’s also no detail whatsoever from the US authorities about how (and if) airlines ought to be checking if an “integrity fee” has been paid and by whom. TIMATIC isn’t, to the best of my knowledge, updated and neither is Amadeus.