If it gets enough light/sun that plants grow, put a peppermint plant out there.
Rodents hate the smell.
If nothing grows there. You could spray peppermint every month, or hook up some kind of rope/ladder for them to get out. If you go the "escape route" way tho, they're gonna live in there having babies and you won't be able to open the window or they get into the building.
Might be better to put a finer mesh over the chicken wire.
Hmm, I can't grow peppermint in the recess, but maybe around the dome would work?
Good point about the escape route possibly making things worse. There's plenty of evidence that previous owners have dealt with rodent issues, so I wouldn't want to reintroduce that possibility.
Probably even be enough to have one inside on the windowsill.
Rodents have an insane sense of smell, and they hate peppermint because the smell is so strong. So it would probably be enough to keep them from going in there.