Thank you for sharing your query about how to remove a screw with a damaged screw head.
One technique to remove a screw with a damaged head is to place a rubber band on top of the screw and place your drill on top of the rubber band and turn. The second option is to use 200mm Combination Pliers. Grab the head of the screw and use it to turn the head until it is halfway out. Once there is enough to hold on to, you can then remove the rest of the screw by hand. The third option is to use Sutton Tools No2 Easy Out Extractor Screw Set.
It often happens that the drill fastening bits we use get rounded and provide no grip or sometimes destroys the head of the screw. I suggest using hardened fastening bits like the Ryobi 50mm PH2 Impact Driving Bits - 2 Pack. It has hardened tips and is rated to last three times longer than ordinary ones.
If you need further assistance, please let us know.