Okay, pardon how pitiful this might seem but:
Perhaps remove the messages 'sent' by pound pets when you trade them away? Or make an option, possibly, to turn those messages off.
They may seem silly or like they can't be a big deal, but frankly, they're really a bit upsetting. Owning multiple pets myself, even considering the idea of abandonment - even for fictional pets, just drawings on a website- can be damaging. Especially like right now, when I have been going through an insane amount of pain following a breakup. Trading away a pound pet without realizing it, but not really wanting it anymore, and receiving that message and knowing what it is really just hurt. It shouldn't have hurt, given that this is only a game, but it can be somewhat damaging if someone is already in a bad spot for it to come up.