We have a 14 bus and I did not know "the trick" but managed to get them out by lifting up the screen and then using a spatula, sliding it under the bottom part of the screen, and then toward me. The larger the screen the easier.
I had a couple screens that started to look worn so I replaced all of them with fresh screen.
Scott and Deanna Brandstetter
2014 Tiffin Allegro Bus 45LP
Domicile and current home, Jacksonville, FL