OK, yes, I think I was on the wrong assumption of your question. Sorry.
But the fact that they can't find your loan in the system isn't really of that much importance - you are already in litigation with them as to the foreclosure. They might remove mortgages from their general computer system when there is foreclosure litigation ongoing - it's a business procedure that's the way they operate.
Clearly they believe they have the right to foreclose on the property - that's why they initiated the foreclosure.
However, to quiet title - goes way beyond your loan not being in their computer system.
An action to quiet title is a lawsuit brought in a court having jurisdiction over land disputes, in order to establish a party's title to real property against anyone and everyone, and thus "quiet" any challenges or claims to the title.
This legal action is "brought to remove a cloud on the title" so that plaintiff and those in privity
with him may forever be free of claims against the property. [Wikipedia]
Given the facts and circumstances you originally stated, only if the mortgage was somehow wrongful or illegal and didn't comply with the law could you possibly file a quiet title action which would probably be revealed in the course of your ongoing litigation with the servicer/lender.
I would contact your attorney and make the insurance claim through them. But that they don't find your mortgage in their computer system could be because of many reasons - the most likely is that because you are in litigation and they don't want their agents or employees to disclose any information about your mortgage loan except through their legal representation - that's most common reason you wouldn't be able to talk to the mortgage company about your mortgage.