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 color to the hat. This can soak up an oil mark. Afterwards, rub the chalk off the hat.
I got the hat for Christmas from my daughter (who happens to be a Nurse Practitioner saving lives daily!). Because of my large melon head I had to return it for the next size up. My replacement hat arrived promptly and in good order. Made from high quality genuine leather, it is the best hat that I have ever owned. I recommend this hat to anyone who wants a great quality hat at a fair price.