I would not shoot through the screens for two reasons
1. you'll ruin your screen (obviously)
2. why take a chance at having something deflect your arrow on your dream buck?
I get that but the qustion remains Why hav screens on these things because if I try to remove them for a shot the deer will hear that velcro rip apart. And what would be the recomended approach should I just leave them off and then do i need to camo my face with paint or a shroud inside the blind... oh and unfortunately i only get one buck a year in Kansas so I am Doe hunting now LOL