M.P.
If the scratches are not too deep you can purchase a repair kit to smooth them out. I've successfully used the inexpensive one that uses a fluid and a cloth. There is a more expensive one with a machine sort of device. I've had a friend fix one that I couldn't fix with the inexpensive one. My grandson deeply scratched one of his favorite DVDs and it could not be fixed.
After the really badly scratched one I stopped letting my grandkids handle the DVD when it was outside the case until they were more mature. At 3 they do not have good enough small muscle control or enough experience to know when what they're doing will damage the DVD. I started letting them with my supervision when they were around 5. When I saw that they were able to be careful I stopped standing by their side.