You mean willing to refund the inspection fee I hope. 
Per the SOP, your responsibility is very limited so you could go that route.
Did they make a demand? Did they ask for the money? If so, your insurance company probably has a requirement you notify them.
And there is also this?
Exactly… Cutting the paper using a razor knife along the joist would provide an exact piece less the paper flaps for stapling. Flip it over and push it back up into the joist pocket. Hire a handyman and it should take no more than a 1/2 day.
Quick question if the service you provided was on September 2020 why in the word they are coming after you , almost a year later ??? I am just curious… is the HI liable after how many years?
I would suggest to the owner they follow these guidelines:
https://www.buildingscience.com/documents/information-sheets/crawlspace-insulation
This is the standard approach in Colorado. Problems can occur in high water situations.
Peter already mentioned it but in case you have not found the form yet, here is a link.
General Release and Plain English Version of General Release - InterNACHI®
When you talk to her and come to an agreement on any compensation for repairs to be done, it is a good idea to have her sign this form so that you will be released from any further obligation.
I used this form a few years ago when a client had a complaint about something and I decided it’s best to pay for a small replacement than to argue about SOP.
Good luck, Let us know how your negotiation goes. Hopefully it is settled amicably.
If you need to install the insulation such that the vapor retarder (the kraft paper side) is up against the warm/moist side, in most North American climates that will be the living space.
However, if you are in South Georgia/AL/MS or in the state of Florida, the odds are that you will have more humidity and heat outside of your living space than inside, at least for the vast majority of days.
In these areas you will often find crawlspace insulation installed “Upside down” to what you are used to seeing up north. In many locations your vapor barrier will be “correct” on some days and incorrect on other days. You can’t realistically flip it every time the weather changes.
Most of us are used to seeing the kraft paper up against the subfloor and drywall of floors walls and ceilings.
Anyway, right or wrong, that’s what the debate is about.
I would never recommend on what I personally think about crawlspace insulation. Only what’s there or not and if it’s installed correctly. I will note if I see any critter infestation or other issues, but I note it only. Let them decide.
See it both ways here my area Bert. I will always call it out for further evaluation and let them fight it out. 
I see it both ways too. Some people don’t realize the paper is a vapor retarder and think it is just a stapling flange.
I’ve seen 1 year in some instances, but it all depends , where you do business, however if you could settle this time and review you contract and add that type clause that could help a little , at least to minimize the worst case scenario down the road … do not forget to get the release signed if you decide to return your fees or pay … General Release and Plain English Version of General Release - InterNACHI®
Thanks bert, you beat me to it.
When you start talking about vapor retarders, and vapor barriers, it opens up another whole debate, based on climate
Thats why I was wondering what climate he was in.
In Florida, I rarely see insulation in a crawl space, unless it is a mobile home, and then you have the whole vapor barrier debate… (typically the vapor retarder is on the bottom side, and unfaced insulation between that and the subfloor)
In my former life I was a licensed Insulation contractor for over 34 years.
Bottom line the insulation if it is paper faced is Very FLAMABLE (it will burn about as fast as Diesel soaked paper) and should be corrected. The correct way to do this would be to flip the insulation so the Paper is UP and in contact with the floor decking and then wire insulation anchors (we called them “lightning rods”) should be used about every 2 feet to hold them in place. If the batts are say R-19 and the joists are 2x6 you could use a twine to hold them up.
I see no reason that you would be liable for a correction past this. No way should you be liable and pay for a greedy contractor to sell an insulation job and material, at inflated prices. I would say 3 hrs labor for each 1000 s.f. and probably $30/1000 s.f. for the wire anchors to make the correction.
In mild areas of Northern California… the flipped vapor barrier is unlikely to ever cause a moisture problem. It’s pretty random which way that stuff is installed around here. It’s a defect, but does not seem like a serious defect.
The vapor barrier burns, but so does wood.
