The color of solid surfaces material (Corian, Hi-Macs, and Avonite etc) goes all the way through these surfaces making them completely renewable and repairable. Homeowners that are good at woodworking and are skilled at using a random orbital sander can remove most minor cuts and scratches. However this is not the place to learn as it will be a very noticeable mistake if not done with care. If in doubt, it’s best to have a professional do this or buy a piece of scrap from a countertop fabricator to practice on.
Judge the severity of the scratch and start with 220 grit auto body quality sandpaper or 60 mic sandpaper on your random orbital sander. Lightly spray water on the counter and keep it wet, this will help keep the dust down. Just keep area wet, not flooded. Check to make sure that your sander is plugged into a GFI protected outlet. Sand in an overlapping pattern and periodically switch direction and sand at 90 degrees. Continue this process until scratch is gone, feathering in the edges of the perimeter.
Wipe down the counters with a damp rag to remove all residue. Continue this process with a gray Scotch-Brite pad on your random orbital sander and go over the entire area, again keeping the area wet to keep dust down. When you have finished, clean off the counter with water. The luster of your solid surface countertop should be restored!