Hello Dowly,
you can polish this out, as long as the scratches are not too deep.
My Rome Total War CD recently did not work, because i had opened the tray with a needle, so the tray was half open and the CD inside uncentered still spinning like mad, being scratched all over during this process - and not scratches from the center, but circular rings - which is really bad .. information is twice on a CD, so a vertical scratch usually does no harm, a problem are circular scratches.
I used car mild polish without applying too much pressure, until the CD began to shine, and - all works again
Good luck,
Catfish