If your hat is stained, a leather dressing can be applied to the outside of the hat. The leather dressing will darken the hat, mask the stain, and make the hat more waterproof. If you're just removing a small mark on the hat, sometimes rubbing the area firmly with your thumb can erase the mark. Also, you can try chalk that is a similar colour to the hat. This can soak up an oil mark. Afterwards, rub the chalk off the hat.
That hat looks great, unfortunately I had to send it back. It doesn’t quite fit my face. I prefer the gambler style. It is very close but the crown is a little bit too short for me short for me. Excellent quality for the price.