and the City gift set from Ebay a pirated copy?

Almost every DVD and DVD Set has a bootleg out there, most come from China and are Region 0. What you pointed out are sure signs of bootlegging. There might be scratches on even new discs, but peeling and melted parts are not going to happen very often, almost never, pealing doesn't happen because they do special printing on DVDs for labels, they are not stickers, and melting doesn't happen very often because this damaged is easily found by the machines they employ for quality urance.