Paint is basically chalk or limestone or calcium which is what we try to remove from pure. As it gets older it oxidises, reverting to what it used to be.
You may get better results by just re-cleaning or rinsing the glass only on a second clean and turning the flow down so that the overspray doesnt go on the paintwork also not touching the top edge or sides too much...
The oxidization- if thats what it is will have dried on the glass now, so they will need re-cleaning as above as the spots and stains are "glued" on. I do many poorly painted windows (my own house)and georgians with this double rinse maybe 5-10 minutes apart just doing glass only. But there does come a point where whatever you do you will get poor results, hopefully the customer will understand if you use tact.
Hope this helps.