Diagnosis
It's not just glass—it's a glass panel with a matte anti-glare coating. Harsh chemicals like ammonia or alcohol in standard glass cleaners will permanently damage and strip that coating, creating cloudy, smeared patches.
How to Fix It
Power off the monitor and let it cool. Use a dry, soft, microfiber cloth (like the kind for glasses or cameras) to gently wipe away dust. For fingerprints or smudges, slightly dampen a part of the microfiber cloth with distilled water only. Wipe gently in a circular motion, 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-specific cleaning solution that explicitly states it's safe for anti-glare coatings. Apply a tiny amount to the cloth, never the screen. Isopropyl alcohol (70% or less) is sometimes recommended for glossy screens, but it's a gamble on this matte coating—I'd avoid it.
Heads Up
Don't use paper towels, tissues, or rough cloths—they can microscratch the coating. The damage from wrong cleaners isn't always immediate; it can appear as a gradual, permanent haze.