Regardless of whether the muggle should or shouldn't take the FTF prize a muggle isn't playing by our rules anyway so if he takes it what can be done about it? Ban the muggle from the geocache community for life?
You don't know who the muggle is/was do you? It is doubtful that a muggle would leave his real name, address, phone #(s), email address, etc. so you can't contact him and demand that he return your property that was left in the woods.