Black spots on mac air logo

The Apple logos on current MacBooks (as well as iPads) are very prone to showing smudges, especially greasy/oily ones. That's what it looks like to me in your photo. Try to wipe it with a microfiber cloth...maybe breathe on it to add some water vapor/moisture. If no microfiber cloth, try a T-shirt or flannel. Once you get it clean, try not to touch it since it will show (as you've seen) smudges and fingerprints very easily.

Try this first since taking it back to Apple will require an additional step and time.

You never said that you tried to wipe it using a damp microfiber cloth...did you? If that is all that is needed, then your solution is in your hands.

Or even try alcohol (which Apple does say is fine to use)

"Is it OK to use a disinfectant on my Apple product? 

Using a 70 percent isopropyl alcohol wipe, 75 percent ethyl alcohol

wipe, or Clorox Disinfecting Wipes, you may gently wipe the hard,

nonporous surfaces of your Apple product, such as the display, keyboard,

or other exterior surfaces. Don't use products containing bleach or

hydrogen peroxide. Avoid getting moisture in any opening, and

don't submerge your Apple product in any cleaning agents. Don't use on

fabric or leather surfaces."

Talk to Apple support. I suggest you start with the "Support" link this page lower left.

Returns & Refunds - Shopping Help - Apple (CA)

Have you tried to gently wipe it off? If yes and no joy .....

Take it back to Apple. You may be still within the "free" return period. Certainly at less than one week it's still under warranty.