Apple Watch Scratches on Screen

Hi,

My Apple Watch Series 3 just arrived last year and I started using it on July 4. Since then, when I’ve played with my dog he’s bitten my watch a bunch of times.. there are a TON of scratches on it.

First, they make the watch look bad, and second, I hope it’s not affecting anything on the inside. So how do I remove these scratches without doing any more damage?