Are you referring to the Google Search bar?
What brightness level do you normally keep your screen at?
Does your screen remain on whenever the phone is charging/docked?
I don't use the Google Search bar; I normally have the screen on minimum brightness (unless I know I'm going to be outside); and I turn the screen off when it's charging/docked. I haven't seen the problem that you describe, but if you normally keep the screen brightness turned way down and don't leave the screen on while charging then I wouldn't expect the Google Search bar to get burned into the display.
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