How to Repair Windows Screen Holes?
Buy or salvage sufficient screen mesh to cover the entire tear. If you have an old, unused screen in storage, you could use this to salvage pieces from. However, if you are concerned about appearance of the screen, it is probably best to try to buy the same kind of screen, either nylon or aluminum, in the same color.
Cut the screen mesh the size of the hole in the torn screen, leaving a one inch (2.5 cm) margin on each side of the cut shape.
Thread a curved upholstery needle with strong thread of the same color as the screen. Alternatively, make the thread as close a match as you can get or try fishing thread, which is invisible and very strong. A straight needle can be used if you have access to both sides of the screen, but it will be more difficult and time consuming.
Cover the tear with the patch of screen mesh that you have already cut. If the screen is still in its window you can hold this repair piece in place temporarily with tape. If you have taken the screen off the window, perform the repair with the screen laying flat.
Stitch around the patch. Take the threaded needle and "sew" by going through both layers of screen. Take small stitches, making sure to pull in all slack. The aim is to bring the two pieces as closely together as possible.
Finish with a strong knot. Tie off the thread with a strong knot, at least double tied. Ensure that there are no gaps where insects can get in.