When was the screen door invented?
I’m not sure exactly when they started using it since sometimes patents come out later than the actual invention but by the 1880’s they were using a “mosquito netting” or “bar netting” on doors in America for sure. I’ve seen reference to it in period books. In the Laura Ingalls Wilder books it is described as being pink. You might have more luck researching netting rather than screen. I’ve also seen references in 1850’s home journals to mosquito netting that was hung around the beds, it was woven out of a gauze. Prior to netting people just shut the door at night since it was commonly believed that night air was what caused what we now know as malaria. They called it “fever and ague” or “ager” or “the shakes”. You could also combat the annoyance of mosquitoes by building a “smudge fire” outside open door. I’ve seen reference to people using a wire screen flap (no frame) in 1830, but it was in India, not America. Metallic screening used in screen doors and windows was patented (#297,382