So, yes, I finally called my mortgage company. And the resolution is completely unclear. She may have been telling me that she can't reduce the amount until the title claim goes through, which is the most sensible of the interpretations.
But I couldn't get a straight answer out of her. In fact, mostly, it seemed that she was telling me that the only process that would function would be foreclosure. Except that every time I asked her if that's what she was saying, she'd back off and mumble.
The phone call ended when I finally said something about how I was glad to know what they could do to protect themselves, I wanted to know what I could do.
The answer? "Get legal advice."