I suspect you have some fine dust caught between the cover glass and the LCD display unit. The static electricity tends to collect it there.
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Sadly there is no guide to walk you though the steps. But there is a Teardown, It should give you enough help to pull the cover glass off (up to Step 3). [https://www.ifixit.com/Teardown/Apple+Thunderbolt+Display+Teardown/6525|Apple Thunderbolt Display Teardown]. Make sure to use reagent quality Isopropyl alcohol with lint free wipes to clean the glass.