And if they want your paper so they can "see your thoughts" (and pay you for the privilege!?), what's wrong with that paper also being entered into Turn It In? After all, you surely don't think they were lying about their intentions. Because if you suspect they are lying about their intentions, then aren't you aiding cheating?
Well, actually you are still breaking the honor code even after you're graduated. Though the school would probably have little recourse against you in practice.