Thrown off where? The ship was far beyond the outermost starbase or Federation outpost. One way or the other, she was committed to being there for the whole mission.
I think you could have had her really screw up during the Mabrae section of the mission and have Picard threatening to kick her off the ship, only for her to then make the solution that she eventually comes up with which convinces him otherwise but then, in the aftermath, I'd have shown more clearly that she's making a concerted effort to fit in with the crew, biting her tongue more often.
I've expressed thoughts on T'Rys elsewhere about how, at various points, it seems like other characters have been dumbed down in order to make her seem like such a wunderkind. And I've read elsewhere at how some people have said the characters very much a Mary Sue (the same allegations people have said about Grimm Vargo in Before Dishonor) - and, at times, this does seem like it could be borderline true.
It's just a shame I'm so disappointed in T'Rys as a character, the other new people who flesh out the crew all seem pretty interesting and cool and I've not got any objections to them (Elfiki, Choudhry or Hegol).
I'd also like, as I have said elsewhere as well, Faur to get some screentime!