You may be getting real scratches on the screen, but be aware that the sapphire-coating on the TS also can appear scratched when it really is just marked. To clean those markings off takes some fairly serious buffing, but you might find the screen was not really scratched and comes out clean again.
There are no screen protectors currently available specifically cut to fit the TS. You could cut one yourself, maybe using that peel-off sticker it shipped with.
Sent from my Nexus 7 using Tapatalk