Insurance Claim Paid Out To Me, Contractor Who Replaced Siding 'undercharged' Me In Final Invoice, Asking For More Money 6 Months Later

Situation is fairly simple. House was damaged, I made a claim, the contractor placed a bid which was given to insurance, they agreed to price, and I was paid out. That contract was solely between myself and my insurance, and was made complete when they paid me.

After my payment I hired the contractor to complete siding and gutter repair to my home. I noticed there was quite a few line items in their bid that wasn't happening or needed to actually complete the job on my home. Things such as $3000 for scaffolding, and many other line items that didn't quite match up to the job perfectly, which is fine by me, as long as the work is done and of good quality.

They complete the job, send me a bill, and the final bill is $10,000 below what I expected. I reviewed the line items on the final invoice versus the original bid, totaled up quite a few things that I know didn't happen or get used, and assumed the $10,000 in my favor was because they actually only charged me for the things they did, rather than what they estimated they would need on the original bid. I pay the final invoice and think nothing of it again, because I had no involvement in their bidding process, the insurance payout(Which was solely between myself and the insurance, the contractor was not apart of it), or their final invoice.

They contacted me this week, after they did an EOY audit they realized their error, and are now claiming that they made an accounting mistake when they sent me my final bill. They are claiming that they had two parts of the bid, the original bid amount, and then the supplemental portion of the bid. They admitted this was an internal mistake and that they had meant to charge me for the original bid PLUS the supplemental bid (because we countered the original estimate from the insurance using their bid), but only charged for the supplemental portion.

They've admitted fault and it was an internal error, I have told them "I don't understand my rights, and I need to speak to an attorney before I discuss this situation."

From my understanding since this was their error, and I paid the final bill in full and never had any control, input, or influence on its outcome, that I am not liable for their mistake and that I don't need to consider a further response until they make an attempt to have an attorney contact me.

I can also prove through their bid that there is about $10,000 in work that never happened on my house, and products/supplies that were not used. It just happen to almost perfectly match up with the price of their error, which is why I didn't assume they made a mistake and simply were honest in what they charged me in the first place.

What are my rights in this situation? It matches up to issues with people being undercharged for things like a store purchase where a employee makes a mistake, but the issue is that this has more 0's in it.