A quit claim deed, often used in divorces, is a non-warranty deed for real
property. It gives whatever ownership rights in the property that a party has to
whomever the quitclaim deed is issued to to that party. They need not have any
ownership rights to issue the quitclaim deed. You could issue a quitclaim deed
for the Whitehouse. You have no ownership rights to the Whitehouse so you would
be giving nothing, which is all that you have.
Attorneys typically have a vested interest you going through with the
divorce. If you and your spouse reconcile the lawyer can lose money. Mediators
on the other hand usually don't have such an interest in the brake up of the
marriage. In most cases, their pay is not directly affected by a reconciliation.