Let's say that I snatch a monster, then use giant trunade. Does the monster go back to the owner?

Yes, why wouldn't it? The monster is still face up on the field, and Snatch Steal is no longer targetting it. So reason would state that it would go back to the controller.

snatch steal is a continuous card, that means once it leaves the field its effect vanishes.

actually.... prism has a point if a book of moon hits a snatched mon the mon stays with the current controller

*tony checks snatch steal*

but you uys are right I wish snatch said "return this monster to your opponents feild if this card is destroyed" that would be another combo to make giant trunade useful

The difference between Book of Moon and Giant Trunade is that the monster is turned F/D, and forgets it was effected by Snatch Steal. With Giant Trunade the monster is still face up, so it still remembers.