We have what appears to be Milspec Screen. The screens are cut to size to fit the inside of the wood trim for each of the hatches.
The screen has .25 inch self adhesive Velcro around the edges of the screens. Then there is a .25 inch piece of self adhesive Velcro around each of the of the hatches just inside of the wood trim.
We've had them for about 25 years and we always leave them in place. We, of course, open them a bit to open or close the hatches.
The Velcro on the screens is the original. We've replaced the self adhesive Velcro on the wood trim every few of years. Sometimes I just use contact cement to keep them in place.
I'd post a picture, but with all of the virus stuff we haven't gotten up to the boat yet.