Go to your Trainer Card (Right under BAG in the in-game Menu). Go tap the little square under the section "GYM LEADERS." You then will see all your medals. The more close to a dark bluish color, the more dusty they are. The more close to a white color, the more clean they are. To dust them off, simply rub the medal with your stylus for a while. It will gradually go from Dark Blue to White to Sparkling.

Submitted by B. Republic (corbinreno)