If you only notice the issue when the laptop is powered off, then don't do anything as you will make the problem much worse when actually using the laptop.
If, however, the delamination is noticeable when actually using the laptop, then I can certainly understand how annoying it can be. In that case you can try using rubbing some baking soda on the display. You need to open the display 90 degrees and set the laptop on its display so that the base of the laptop is in the air so you have the display sitting on a flat solid surface. You will need to dampen the baking soda just a very small bit and use paper towel to rub the baking soda on the screen. You don't want to have any puddles of water on the screen or the water will seep beneath the glass and damage the LCD panel. If you press too hard you can crack the glass or LCD Panel. You do this at your own risk of damaging the laptop or making the delamination issue worse without completely removing the anti-glare coating.
The baking soda has enough hardness/roughness to somewhat affect the anti-glare coating, but not enough hardness/roughness to scratch the glass. I found this suggestion online and have used it on one laptop screen where the delamination was on the center of the screen and was affecting normal use of the screen. However, it was a very time consuming process and still left some small areas of the coating behind. Of course without the coating the screen is more reflective and the colors may appear a bit different as well since they are no longer being filtered by the anti-glare coating.
Afterwards you will need to wipe off the baking soda residue (takes a bit of effort), then clean the display normally with a microfiber cloth (may require a little bit of LCD screen cleaner as well to assist removing the remaining baking soda residue).
I suggest you only try this method if you are unable to use the laptop and will be recycle it otherwise due to this issue. I tried other methods including the use of chemicals with limited success. The baking soda option was able to remove the remaining coating.
