It sounds really fishy to me. I recommend looking up the company's contact information using Google and ask them about it. They may have no idea this is happening because whoever contacted you is a scammer.
There are quite a few things wrong here. I recently dealt with insurance to fix some damage to my house, so this is fresh in my mind.
Repairs that involve an insurance company usually work one of two ways:
You make the claim to the insurance company, the insurance company sends you the money, and you pay the contractor to make the repairs
You make the claim to the insurance company, and the insurance company directly arranges with the contractor to make the repairs and pays the contractor directly
It never happens where the contractor makes any kind of claim to the insurance company and the insurance company sends the check to you.
After the damages are repaired and that's confirmed by either you or an inspection by the insurance company, nobody is going to be able to make further claims. That case is closed.
So that's one thing that sounds completely off.
The next thing is that the communication should really be in written form. They need to document why they suddenly need extra money and if they ever go to court over it, they need proof that they attempted to collect the money from you. That involves physical written notices (not emails or anything like that) and proof that they were delivered. So phone calls are also suspicious.
Finally, no court will ever uphold some contractor coming after you for money long after the repairs were complete and the invoice was paid. There presumably was some kind of itemized invoice when the repairs were made and that was paid.
So the whole thing smells of scam: the original company probably didn't even contact you. It sounds to me like either someone shady bought the company or (what's more likely) they got a hold of the company's records, perhaps from malware on the company's computers.
My guess is that they are asking you to submit payment in manner that would make it possible for anonymous scammers to receive it.