Is there a way to well, kind of 'delete' a pet from the game? Is their a way to do it? Or do you just have to send it to the pound?

You can send them to the Reserve, which preserves the pet's profile and allows you to still view it, but the pet is no longer usable in-game. Or you can send them to the State Portal Sevice Branch, which completely removes the pet from the game, and gives you extra explores for each one you send. Both are buildings you have to build in order for that option to be available.

Okay thanks!