Some model# helps.
the screws are holding the top down and are under the covering ring
An Frigidaire/WhiteWestinghouse/Tappen range?
These where bad for having 3 small screws beside the burners that had to be removed to lift off the cooktop panal. These always got welded into place. Most broke off and we had to replace the burner heads and screws if we needed to remove the cooktop for a repair. Might be able to drill out the holes on the ones that break off, but I haven't had much success doing that as the screw is hardened and the burner head they screw into is not.
Might be able to clean up those spots with an oven cleaner?!!?