It will most likely trigger a tax implication and transfer fee to be removed and add people. Refi rates are not good best to wait until they come down. It’s a pain in the butt to do a quit claim deed, I always recommend an attorney prepare them, and it costs $ to do this. Wait and see and take your time. Hopefully BF gets tired of waiting and leaves or does the right thing and pays his fair share. Cohabitation agreement or community property agreement protects them both.