I finally got around to asking the property management company if I could install a screen door on my mother-in-law cottage, and they have to ask the owner but it at least wasn’t something they knew to be an automatic denial. Originally I’d thought I’d need a storm door, which isn’t cheap, but realized this morning I just need a basic wood or even vinyl screen door and already have found several which slat the bottom third to prevent any pet-through-screen escapes.