DIAGNOSIS: You're right to be careful. The monitor has a standard matte anti-glare coating that can be damaged by harsh chemicals or excessive pressure.
FIX: Power off the monitor. Use a clean, dry, soft microfiber cloth (like the kind for glasses or lenses) and gently wipe the screen in a circular motion. For fingerprints or smudges, slightly dampen a corner of the microfiber cloth with distilled water only. Wipe gently, then immediately dry the area with the dry part of the cloth. Never spray liquid directly onto the screen.
IF THAT DIDN'T WORK: For stubborn spots, you can use a monitor-safe screen cleaning solution, but it's risky. If you must, apply a tiny amount of a solution specifically labeled safe for LCD/LED screens with anti-glare coatings (not glass cleaner or Windex) to the microfiber cloth, not the screen. Test on a small corner first.
HEADS UP: Never use paper towels, tissues, or rough cloths, as they can scratch the coating. Avoid alcohol, ammonia, or acetone-based cleaners—they can permanently degrade the anti-glare layer, leaving a hazy, smeared, or discolored patch that you cannot fix.