OK here you go into the dark side of baking cakes.
You need to have a contract that you print twice--both parties sign both, you keep one copy, customer gets the other copy. Your contract must state that the cake and the table MUST NOT be moved after you place the cake at the party site.
Very few people know how to move a cake safely...even restaurant staff don't know. I delivered my own wedding cake to a hotel and they broke the base plate when they moved it.
Good thing you have a picture, it is also very important to take that picture of the cake in place.
DO NOT GIVE THIS CUSTOMER ANY MONEY BACK. Even if you have no written contract, you have proof that you delivered a cake in good condition. End of story.