We have mice enter the house each fall, and here is my remedy if the cat has done his job. Get the small plastic rectangular traps and put a saltine cracker with a bit of peanut butter on it in it at the back. The mouse will go in to get the PB and not be able to get out. When I’ve caught him I take him to a nearby power line area with plenty of cover away from houses,and let him lose.
I then wash and repeat to get his brother or sister–there’s always more than one! I’m sure it sound silly but I don’t like to kill them, even though I realize a predator may well get them where I let them lose.