The Greeks haven’t had much luck getting the Elgin Marbles back from Britain. If I (as a US citizen) found a section of the Parthenon some ancestor had secreted away, and put it up for auction, could the Greeks come after me successfully or, like the British, could I tell them to go take a leap?
If you put it up for auction, then anyone, including the Greek government, could make a high bid.
I assume you mean, could the Greek government demand (and get) it back for nothing. I think they would have to sue you in the US courts, and it would be up to the court to decide.