I ventured onto these forums for exactly the same answer. Because they also appear with game events, I now have a collection of 17 pets and no known way of getting rid of them, apart from leaving them to clutter up my inventory. Tried everything, including the garbage bins. When dragged outside the gate, they simply walk back in again. We need a 'send to animal shelter' option. Preferably, they should age and die, as do the little peeps.

On a humorous note .... 17 pets descending on the dinner table when the little peeps sit down to a meal is nothing short of hilarious.