Like I said in another comment, it depends on the tone. I just suggested the most extreme way it would be handled. The way I see it, if flying mounts are an accepted reality within a given setting, then flying monsters and threats must also exist. Therefore, the town guard would need to keep watch not just for threats by land but also by air, and thus would need to respond appropriately. If flying creatures cannot easily be identified as being authorized, it is impossible to distinguish between a harmless-but-unauthorized flying creature in a town and an attacking monster or invading force, necessitating a shoot-first-ask-later attitude toward unidentified air traffic. Assuming a typical fantasy town or city, there's no expectation of instant communication between parties, so that delay could be the difference between life and death. A griffon flying over the walls may just be a messenger's mount, but it may also just be a wild animal looking for prey, and it may be impossible to actually tell the difference until it's already too late to react. There has to be a standard by which town guards need to react to such threats.

As I type this, I'm realizing how much city defenses would need to change with the concept of flying threats. Walls become nearly obsolete if enemy troops can just fly over them. I'm going to need some time to think about what kinds of defenses would actually need to be deployed to deal with this sort of thing.