Usually, screw heads are rusted and when you stick your phillips screwdriver in, it strips out head. What I do, in this case, is take my dremmel with a carbide cutting wheel, and cut a new flathead screw slit into the screw top. On the cooktop, the slit usually works. ]
On Stove ignitors, I too take a little wire brush (similar to toothbrush but with wire bristels ) and water and scrub the screw threads. 99 percent of time, this works and only takes a little time.