How do I deed the property back to the bank or whoever is holding the mortgage?

What do you think that will get you? First the lender has to accept it, no reason for them to do so. Second, if they do, you still owe the balance on the mortgage. They will sell the propery at auction and go after you for the balance.

What's the real problem here?

It is a question being debated by a lot of people, there is no specific problem.

Why would there be debate? What people?