Diagnosis
That fabric cover is a dust magnet, but it's designed to be cleaned. The main risk is getting moisture into the top touch surface or the base.
How to Fix It
Unplug it first. Use a slightly damp, lint-free microfiber cloth—just damp, not wet. Gently wipe the fabric in one direction to lift the dust. For tougher spots, a very small amount of mild soap on the cloth can help. Never spray cleaner directly onto it. Wipe the glossy plastic top with a dry part of the cloth.
If That Didn't Work
For ingrained dirt, you can use a soft-bristled brush (like a clean, dry toothbrush) to gently loosen debris from the mesh before wiping. A can of compressed air held upright can also blow dust out, but keep it brief and don't tilt the can.
Heads Up
Never submerge it, run it under water, or use abrasive cleaners, window cleaners, or solvents. And absolutely do not try to remove the fabric cover—it's glued on and you will break the internal ribbon cables.