You can't delete a pet but if you don't take care for it, it will run away which is basically deleting a pet.
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You cant delete a club penguin account
When you're on the main menu of club penguin game day, click 'Options' and then 'Delete Penguin'. Select your penguin and simply delete it from club penguin game day.
At the pet shop!
puffle2012
you cant delete items on club penguin that you already bought. those you keep forever.