How can I clean a thumb smug-mark on the screen?

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Try this way to clean your TV screen:

1. Turn off and unplug your TV.
2. First try using a dry, anti-static cloth and rubbing gently.
3. Use water to lightly moisten a clean, soft, dry cloth, and then rub the
   screen gently. Do not let the water run down the screen or enter behind
   the screen frame.
4. Wipe with a dry cloth after cleaning.

Important: Rub as gently as possible. LED screens can be damaged if you press too hard.
WARNING: Never use any type of window cleaner, alcohol, soap, scouring powder, or any cleanser that contains solvents. Never use abrasive pads or paper towels. These can scratch the screen causing permanent damage.

Did you wipe with a dry cloth after cleaning?

It's not necessary. Your TV needs to be unplugged.

You can use a flashlight on your phone.

Now, re-do these steps, please:

1. Use water to lightly moisten a clean, soft, dry cloth, and then rub the
   screen gently. Do not let the water run down the screen or enter behind
   the screen frame.
2. Wipe with a dry cloth after cleaning.

Tell me once it's done, please.

Do you have a micro-fiber cloth?

Good.

When you get it, repeat these steps again, please:

1. First try using a dry, anti-static cloth and rubbing gently.
2. Use water to lightly moisten a clean, soft, dry cloth, and then rub the
   screen gently. Do not let water run down screen or enter behind screen
   frame.
3. Wipe with a dry cloth after cleaning.

Is there anything else I can do for you today?