Had a few of these of the years, loads of money, loads of time, need their self importance to be re-energised to the level they used to be at when they worked for a living!
If they take you to a small claims you can still not pay even if they find you wrong which will entail even more hassle for them to escalate it to a higher court, depends if you want to take the chance.
I would generally pass all correspondance to the insurers stating you followed manufacturer's instructions (if you did?), did the pads come with the mirror?
If they supplied them and they weren't correct it could be argued that you are the competant person (as you agreed to fit it) and made a mistake, (if they gave you sticky pads to fit a boiler they'd also supplied you with wouldn't fit it but you did fit the mirror); and i'm not having a dig, just stating what they'll probably argue......
What i've learned to do is use a simple quotesheet that has all the terms and conditions on the rear so i'm covered with their signature of agreement even before I start work. If the job changes I use the variation sheet so I'm still covered, and they still have to sign for the variation (I also tell them this is standard practice and I need to do it to get my insurance company discounts, not that I do!!!).
If there's something not in the terms and conditions that is specific to this job then I add it to cover me. My son who's a chippy has also altered the sheet (as it's a gas one) and it's got him out of the preverbial a few times as the customer can't argue what they've signed for!
I got them from here:
Gas Forms: Quotation Acceptance Form
Gas Forms: Quotation Variation Form