Assuming you're talking about portlights?
A picture would help, but it sounds like your screens are glued to the inside of the frame and then the rubber seals are stuck (they come peel-n-stick) onto the screen. Meaning, the screen is sandwiched between the frame and the seals. If you want, you can get new seals that have a groove in them to accept a stand-alone, plastic-framed screen that pops in and out. This is assuming you have Bomar/Pompanette portlights.