I used to be in the glass industry for a while.
There is something called Jewellers Rouge that we used to use on ordinary annealed glass (every day glass).
But as your window is toughened it is likely to pop with the heat thats generated in the polishing.
Its an awkward one this, see if you can get a second hand replacement?
ps. Not sure if Anger can help.
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Keep it on the black stuff and leave the pit boards alone 
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