In our PrepExcellence course portion regarding reconditioning of used cars we addressed the "ghosting" images left when a crayon was used to put on a price or such.
Normal cleaning of the glass would leave a "ghost" of the number, etc and under certain conditions the image was still visable.
Chatted with my contacts at PPG regarding this and they put me in touch with some folks at their automotive glass division.
After explaining the concern, they sent me a a set highly magnified photos of automotive glass.
Under magnification, it looks like a mountain range, dips and valley's, highs and lows.
It may be "felt" using a cellophane wrapper over your fingers, "some times'.
After I saw these, did some thinking, figured it out.
We taught to spray the affected areas with our Omni All Purpose or New Car Prep, if we knew which type of marker was used.
Some are a wax based, others are more of "chalk" type, most of the time one does not know which.
So, spray with the Omni, then agitate the area with a velour spotting brush after a 2 to 3 minute or longer dwell time.
If the Omni didn't get it removed, move on to the New Car Prep, do the same, then wash off with soap and water or glass cleaner, dry. inspect.
What is going on is this.
The crayon/marker deposited minute amounts of the marker down into the microscopic hills and valley's of the glass, when then picked up the light rays and allowed one to observe the "ghosting" effect.
By using this process, with the brush, the residue of the marker is removed and the "ghosting" is gone.
One could use an old tooth brush for this process, just that it will not evenly cover and remove as evenly the area.
The issue that started this thread is most likely a "deposit" of the adhesive used to adhere the sticker/decal to the window.
That would require the "removal" of the residue from the "hills and valley's" of the glass.
Grumpy