Shouldn't even need to remove it -
eject the magazine, arm yourself with a cottonbud and something like MrMuscle orange-action (or alcohol if you have it) .... anything grease-cutting
To the back, left of the changer slot (nr. the lens) there are a couple of white plastic guides - poke the cotton bud dipped in your choice of solvent between these a few times, allow to dry, and start enjoying your CDs again