Probably worth taking to a gunsmith. He would probably have it out in a few minutes. Will be money well spent.Guys, thanks for all the suggestions.
My BT99 is old so it's not Browning's problem.
I am pretty sure the screw is hardened steel and I don't have a "mill vise". I do have a drill press but it is very old and there is a lot of wobble in the quill. I don't think it will drill a hole straight enough to work.