Don't just sand though add some wood putty in to fill in voids where there is wood missing and then sand that flush with the rest of the wood after it dries if you need to. If you can get a quarter size piece of the paint up you can take it to a paint store and the can match the color. It won't be perfect but it should be close. Better yet they have colored wood putty and if you can find a close enough match you can save yourself the cost and trouble of painting. If it is just narrow scratches you may be surprised how little it shows even if the colors don’t match perfectly.

When I lived in base housing my puppy ate a corner off of our stained wooden cabinets and I was able to repair it so they never noticed. It really isn’t that hard just think of it as an art project.

Do be careful though that you are not making things worse. If you take off to much paint while sanding you may end up having to repaint the entire floor.