Cheese maybe one of the food mouse eat, it doesn't mean they love cheese as their Favourite Food.
In Fact, Mice enjoy food that are rich in sugar as well as peanut butter and breakfast cereals. So a Snickers bar would go down much better than a lump of cheddar.
So the next time you want to setup a mouse trap, do consider using peanut butter and breakfast cereals instead. The results may turn out BETTER than using a Cheese.