Our house came without a screen door, so we’ve always had problems with bugs flying in if we left the back door open for ventilation while we’re home. We bought one of these at a show stall recently and it seems to work pretty well: Magic Mesh.
It attaches to the door frame with velcro strips so it can easily be removed in winter, and magnets hold the two sides together. It was a slightly tricky fit on our door because the frame is narrower than the mesh, but I had it up there in about fifteen minutes and it hasn’t fallen off yet. Either way, it has to be much better than leaving the door open with nothing to stop bugs flying in.
I’ll be interested to see how well the velcro survives the first major rain storm. The glue seems pretty tough so I’m hoping it will hold together. If not, we can always buy new strips to replace them.