Two mishnayot! When an idolator brings an offering in the Temple... yes, that turns out to be something that could happen. Jewish people can't get benefit from those offerings, but there's no "misuse" of consecretion in those offerings. Likewise, there's no concern of impurity or exchanging the offering. The Gemara, of course, has some level of dispute over the stringencies applied to this kind of case. Also, those practices that were not subject to a violation of pigul may still be relevant for concerns of "notar" - leftovers, in terms of timing - and impurity.
