Are you sure it is glass? Mine definitely seems like acrylic. It has rounded corners, can you do that with glass?
If you want to take a scratch out i would think to approach it like car paint. Start with 2500grit wet sand (sand in one direction at an semi perpendicular angle to the scratch), then 3000grit in the other direction. Then follow up with a mild scratch polish to remove the dullness that the sand paper brought on. I usually use a Dual action polisher for this last part.