Do you think Peeta was lying when he said that the capitol doesn't own him that he's just a piece in their games or do you think he was telling the truth and making a joke what do you think please help

I think that Peeta has the whole "games" ideology worked out early in the book. He understands that he, like the other tributes, are disposable. They are just a piece of the Capitol's machinery used to influence and control people.