Hit the Road
The mice need to go, however you can do it. We had mice at Liberty wildlife years ago, they would come at night and kill our orphans, we found many headless, babies and babies that look like your pidge. They chewed through thru the soft wire on the encloses and thru the " rubbermaid " containers we kept the tiny babies in..we killed them,,sorry, but, baby songbirds, kestrel, hummingbirds are way more important to us..
I had mice as pets when I was little so I take a different view. I had no idea that they actually attack other animals. This whole post has been an eye opener for me. Let's hope this is a one off and not a whole family of mice living around the aviary.