I haven't actually tried this, because I haven't got around to fooling around with audio editing beyond using GarageBand or some of the other DAW's, but you might want to download Audacity (free, and works with Macs and PC's, I think), and import the CD track you're working with, and work on it there before exporting to GB.
Now, this is just a guess because I haven't read anything about Audacity for a while and can't remember the music file formats it imports from and exports to, but this might be a possibility for helping you edit the file to reduce the noise that you're hearing.
All the best,
GVDV