How do I remove dirt from the illuminated apple on the chassis?

Thanks for the link, but I've read that already and followed the instructions. They worked wonderfully for cleaning everything except the things I've described above - the dirt is embedded in the edges such that a cloth cannot pick it up.

Edit: here's an image that clarifies better, though my phone camera's not adequately representing the darkness of the buildup, to the point where much of it hasn't been picked up at all.

Save your sigh, it doesn't suggest that anywhere on the page you linked to me and I've already made it clear I have no frame of reference on what to do. I'll try a compressed air duster in the morning when I can go pick one up.

For reference:

"Portables

MacBook, MacBook Pro, and MacBook Air

When cleaning the outside of your MacBook, MacBook Pro, or MacBook Air, first shut down your computer and unplug the power adapter. Then use a damp, soft, lint-free cloth to clean the computer's exterior. Avoid getting moisture in any openings. Do not spray liquid directly on the computer. Don't use aerosol sprays, solvents, abrasives, or cleaners containing hydrogen peroxide that might damage the finish.

To clean the screen on your MacBook, MacBook Pro, or MacBook Air, first shut down the computer and unplug the power adapter. Dampen the included cleaning cloth with just water and wipe the screen. Do not spray liquid directly onto the screen."

THAT is what is on the page you linked to me. I have done all of those things. They have fixed a number of my problems. They have not fixed the problem I am inquiring about.

Thank you for your time! Maybe in the future you'll learn to be less rude to people who don't know as much as you, or, alternatively, you'll learn to read through the links you send before attempting to make others feel bad for not catching information that was never provided.