Hi,
Start by squirting wood restorer into each screw hole. Get as much in as you can.
After it has cured fill each of the holes with leather (cut in a triangular shape) after squirting the hole with some slow cure CA glue for wood. Wait until the glue cures then use an exacto knife to cut any protruding leather off flush to the surface. Insert the screws flush to the surface and let them stay overnight. Now remove each screw and as you do so give the hole a squirt of water thin CA glue. This will preserve the "threads" the screws have cut into the leather.
The above is how hardwood "rails" on Steinway grand pianos are renewed if an over enthusiastic technician strips a hole.
Reinstall the awning. When putting in the screws, turn them backwards first until you feel them go "click" into the threads you have cut. When the screws are one turn from fully tightened put a dab of dicor at the top. Finish tightening and wipe away the excess dicor.