Im sorry, I should have specified. If I send my card to their GY, then banish it, where does it go? I would assume that it goes in mine, since it is my card originally. Like how Kaijus go to my GY when destroyed, even tho they were on my opponent's field.
My TCG understanding is non-existent so you'd probably be better off hearing from someone else but I'd like to think it goes to whoever's graveyard it is in but again I'm just thinking from a "side" perspective.