Best way to deal with this is to not go on the defensive. I was accused of scratching some very old crittle glass once. I simply said, oh right ok, lets have a look then. And after looking, yes there was scratches on the glass and i simply asked the householder did you actually see the brush scratch the glass, and are you 100% sure that the action of cleaning has scratched the glass? Can you please show me how you think the brush scratched it. Honestly speaking she couldnt. Now i didn't go on the defensive, i asked her to reason on the subject.
I said to her we had better check the brush over, so we checked it over for grit, she could see that the only real way any scratches could have been made was if i had dipped the brush on the driveway, and we couldnt find any abrasive materials on the brush.
We finally looked at the rest of the windows, and couldn't find any further scratches, so she came to her own conclusion that it was very unlikely that I had scratched the glass, and even if i did we both agreed that she couldn't with 100% confidence insist that i had scratched the glass, as i couldn't with 100% confidence disprove it either.
I asked her at that point would she like me to carry on cleaning, and she said yes. I then said lets monitor it and if you think or can see that any new scratches happening ill stop immediately. So she followed me around from inside and i asked her to signal if she thought any damage was happening after this she satisfied herself that the brush was fine.
Now i cant prove or disprove, weather i did scratch the glass ir not, neither can she... the important thing is i gave the customer time to fully understand the scenario, to investigate the probability, and be objective about the situation.