how do you remove scratches from a watch face?

Answer 1

You can try toothpaste mixed with a little water. Then polish with a soft cloth or use a Dremel with the buffing wheel.

Answer 2

I don't know of any good way to do this without sending the watch back to the company that made it. But that is really only an option if the company is US based. (You are in the US, right?)

I have never heard of devices that are safe and easy to use that are available to consumers.