Healing only works with discard and poison/diseases, you cannot heal a capture, set aside, convert, remove from the game, return to hand, or shuffle ability. If you have a heal enhancement in your hand at the time you can heal immediately when the character is discarded (though the battle is still over if they were discarded from there), otherwise you can heal them anytime after that during the same turn. Poisons/diseases can be healed anytime after they are put on a character.