Maybe you could try cover the vent with some mesh with holes large enough not to restrict ventilation, but small enough that the mice cannot get through.
Stuff some steel wool in the louvres. The air can still pass thru, but mice won't be able to.
I bought a plastic cover that just screws into the wall. It covers it but has small slits for the air to vent so nothing can get through it. Very cheap fix.
Attach a piece of metal window screening to the pipe. Just make sure to clean the lint so the vent does not get clogged, or it can pose a fire hazard.