Cleaning mushrooms is a tiny bit tedious but very easy to do. Just use a damp paper towel to wipe off any dirt. It is that easy! If you were to put the mushrooms in a colander and rinse under water then the mushrooms would get a little water logged. This is not a good thing.
You may need to use several damp paper towels depending on how much dirt is on the mushrooms.
The mushroom on the left has not been cleaned. The one on the right has....I also remove the stems because they are usually tough.