Screw heads are stuffed with caulking and cannot unscrew. What is the best approach to take down backer boards?
I'm confused by the issue. Why was caulking put on this? Are you sure it's not thinset?
As previously stated, a metal bit should be able to be inserted into phillips head screw.
Why do you need to remove the board?
"They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety."
B. Franklin 1759