Hi Ted,
This I assume is on the PT? They can be a problem and sometimes I can get them drilled out, sometimes I can't . A couple of times I have had to resort to hacking the cowl up just leaving a bit of plastic around the screw and then getting in with the grinder and cutting the screw off flush with the top of the starter housing, then drill and re-tap the thread. As I have plenty of cowls it is not a problem to me. I would be a bit reluctant if it was one of the later cowls but in the end you have to get it off somehow