Am trying out pet screen as a bug screen when camping. Pet screen is sold in the doggie door aisle at the Home Improvement store. Also sold in some fabric stores - many beach tote bags are sewn from pet screen. My window screen is held in place by magnets. Sewed a 2 inch square of pet screen over each magnet. Used velcro along the edge of plastic where the window joins the non opening wing area of glass.
I tried to sew sticky back velcro to the pet screen but ran into a lot of problems as the glue from the velcro clogged my sewing machne needle. Instead, I sewed regular velcro to the pet screen and then used simple little glue dots (sold at the craft or stationary store) to adhere the corresponding piece of velcro to the vertical plastic trim. Easily removed - easily put into place. Not sure yet if pet screen works with mosquitos as we don't have mosquitos where I live.