I have used a sliding glass door at multiple homes as white boards and they work fine until my wife used a no fog cleaner then both brands of pens did like yours.
DO NOT SAND!
Use a stronger solvent, when people accidentally use a sharpie on a white board acetone will usually take it off, as I mentioned in my comment start with a weaker solvent, and work up, I suggest solvents not acids some acids can etch glass and you do not want the surface of the glass damaged if scratches are in the surface it will not work as well as the scratches will hold the dry erase marker.
I was able to use acetone and it worked fine. On windshields rear view mirror mount kits come with MEK to strip the glass this would be the strongest solvent that should be needed for glass.