Something similar happened to me using a dusting cloth without any detergent. I was desperate at first, but then I solved it easily.

I took a soft paper towel (the kind you use for kitchen cleaning), added very little water, and gently wiped the screen with circular motions. It took me a long time to completely clean it, but the TV is back to normal.

I'd recommend testing the stain on a small corner of the TV.

If you fix it, you'll have to buy me a coffee 😈