I'd remove the screen to let him out if trapped & to make the spot less habitable if he's decided to set up house.
If you have Pets, keep them away from it. Bats like darkness when they sleep in the daytime, and in-between a screen & window wouldn't have been a great choice. He may be sick. Put on gloves before going near - garden or work gloves, not cleaning gloves. If you remove the screen & he's dead or dying, scoop him into a box & don't touch the box where he touched it. Put it in a cool place (the garage) so he'll suffer as little as possible as he passes. When it's dead, put it in a trash bag, wrap securely and throw away. Throw any gloves you used away too.
If you have a game & fish department, call them before you touch it or move the screen. Explain everything to them. They may come out and get it.
Bats are a main carrier of rabies and many times when they are acting strange they have it and are disoriented. The virus lives in their saliva and bats lick themselves to keep clean. All people who handle bats get the rabies vaccine first. Don't take a chance. Be VERY careful when around the bat. Throw away everything he touched or you touched him with. Spray down the screen, glass and immediate surroundings with strong bleach water. Rinse off after 30 minutes, treat again, rinse & let air dry.