Cut a square hole around the tear using a straightedge and sharp utility knife. Maintain the hole as little as possible and leave at 1/2 in. Of old Fiberglass Window Screen beside the metallic framework.
If you're fed up with the mosquitoes buzzing around your head and keeping you awake all night, how about fixing the screen? Patches will be visible and can look a bit tacky, so if the tear is large or the Fiberglass Screen is in a highly visible area, replace the entire screen. Otherwise, take 20 minutes and just patch the hole.
If your Window Screen Mesh is fiberglass (it will feel like cloth ), purchase 1/2 ft. of fresh fiberglass viewing off the roster in the hardware store or home center or request a couple of tiny cutoffs. Additionally pick up either a rubber-based adhesive or Super Glue Gel. Then follow Photos 2 and 1. The Trick to a nice-looking fix is holding the straightedge closely against the workbench so you can make a clean cutout.