I adopted Vimic from the Adopt R Us and he came with a custom overlay attached. I feel bad for 'using' someone else's art, so, is there a way to take it off? Thanks!

Go here and you should see an option to delete the overlay.
I don't see it... Maybe that's because I'm not the owner of the overlay?

Yeah you wouldn't be able to see it since you are not the owner of the uploaded overlay. Perhaps file a ticket to see if Staff can clear it for you?
it's probably that you can't unassign the overlay because it's not actually in your 'bucket' because you're not the one who uploaded it. you could always file a ticket and see if a staff member can remove it for you.
[edit]bluh nevermind, beaten to the punch