To abandon (3) or store (2) a petz, you will need to visit the petz' profile and click the pencil (1) icon.

(2) Store: Pay 100 coinz to store the petz. It will no longer count against your total petz space, but you cannot play with it or enter it in contests until you have taken it back out.
(3) Abandon: This will abandon the petz and send it to the Pound. If you are the pixer, you can then retrieve it from the Pound for 100 coinz. Otherwise, it is in the pound forever.