Seems early for this corian to be "covered in scratches".
If they were there when you moved in, then the material was
more of a "second" with imperfections. You should have been told about it. If they appeared later, then usually it is because someone hase been cutting on the corian. Corian is a good material for kitchens/baths etc, but there are limits.
Cutting with a knife, GENTLY, usually is not a problem for an adult. Kids, another matter altogether. SOMEONE has used it more like a cutting board, thus the scratches. You do need to "repair" it, not so much for looks, but bacteria will grow in those grooved areas, just like they would on a wood cutting board, or any scratched service. You could soak it in bleach after every use, but that would get tedious very fast. Over time the grooves would also stain. Sorry, too much information!
GOOD NEWS- It actually does not matter that it is "covered" in scratches, because the remedy involves VERY lightly sanding with very fine grit material the entire top. This is because there is a slight change to the finish and you really cannot do just a small section. Lots of things you/your family can do themselves, but make sure you know what you are doing. Of course, if you were to try, and goof it up, you just end up called a carpenter/handyman to do it over. Then again, if you use a hand sander and lose control where it flies into a cabinet..............well you get the picture :(
C., AIA
Green Architectural