Ok – first those are often broken from being over
tightened so they are somewhat fragile. If the pad
is off you could drill a hole in a piece of wood
and slip the transom screw into it to support the
bracket then smack the transom screw with a
hammer several times to break the threads free.
If the pad is on you will need to find a different
way to support the bracket. The farther in the
screw is the more options you will have. I would
heat the piece first. It would be helpful it you
could strike the transom screw in both directions
but that doesn’t seem possible.
A "Boathouse Repair" is one thats done without having tools or the skills to do it properly.