warm it up with a hairdrier / heatshrink gun if you have one. if that doesn't shift it, they're usually on an adhesive foam pad (to allow it to flex and match the screen) so you can get a scalpel under there. once it's off, a scalpel blade will remove the bulk of the goo and t-cut will finish it off. this is what i've always done and never damaged a screen..... yet....
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It does not look like it but the mounting pad is just a little smaller than the the diamiter of a tin can so you could not get a scalpel right the way to the center.
I dont own a heatshrink gun and certainly not a hairdrier
if you twist the mounting with the same motion as adjusting a heater hot/cold dial in an E30 , the aerial will tear off the sticky pad. The suggestion of using a hairdryer is the best advice