Hi
It is possible that you have only scratched through the fingerprint-resistant, oil repellent coating. It is normal for this coating to wear away under normal use, but it may have become scratched without damaging the screen beneath.
Whether you have scratched the screen or not, Apple does not recommend using cleaning products or polishing or buffing the watch with abrasives; these will wear away the coating and may also (further) scratch the display.
Cosmetic damage, including scratches, is not covered under the One Year Limited Warranty (or AppleCare+).
Apple does not offer a screen repair service for Apple Watch. Your watch may be eligible for chargeable, out-of-warranty service. Contact Apple Support (mail-in service may be available), make a Genius Bar reservation or visit an Apple Authorised Service Provider with a view to having your watch checked and to establish any available service options, likely timescales and cost:
- Contact - Official Apple Support
- https://twitter.com/applesupport
- http://www.apple.com/retail/geniusbar/
- https://locate.apple.com
Otherwise, a good quality screen protector (of the thin film type) may be effective in obscuring or reducing the visibility of the marks, as well as in providing some measure of protection against future damage. You may wish to consider, for example: