David Malki drew this!
I don't think putting it into the hand of the person who tried to get rid of it would be the correct answer as that would enable an infinite loop for the player with Cap to draw his entire deck if the original owner of the wound kept using the Grievous Wounds Healing ability.
I would probably KO it. If you do have it go back to the original player then it should probably go to their discard pile.
That's a very good point that I hadn't thought of. It might be too much to hope for an official ruling, but you never know.