Diagnosis
You're right to be careful. These screens have anti-glare and anti-reflection coatings that can be damaged by harsh chemicals or abrasive cloths.
How to Fix It
Use the two-cloth method. 1) First, turn the TV off so you can see streaks and dust. 2) Use a clean, dry, ultra-soft microfiber cloth (like for glasses or camera lenses) to gently wipe away loose dust in a single direction. 3) For fingerprints or smudges, slightly dampen a second microfiber cloth with distilled water only. Wring it out completely—it should be barely damp, not wet. 4) Gently wipe the smudged area, then immediately follow with the dry cloth to buff away any moisture.
If That Didn't Work
For stubborn spots, you can use a drop of white vinegar mixed with distilled water (50/50) on your damp cloth. Test it on a small, inconspicuous corner of the screen bezel first. Never spray liquid directly onto the screen.
Heads Up
Never use window cleaner, alcohol, ammonia, or any all-purpose spray. Paper towels, napkins, or rough cloths can cause fine scratches. The goal is to lift debris, not scrub it.