IPhone 5s Case left a ring stain?

I have a iPhone 5s otter box shock prof case, and I had the case on for almost a wile (5-6months) and now I finally took off the case and has a open circle to show the apple logo and that open spot left a obvious circle stain and I had thought it was like dirt that had been left inside but it left the circle mark around the apple logo! "Does anyone know how to take it off?

Clean the phone with a soft cloth adding a little toothpaste diluted with water.