If they can't track their current site, then you are right, they don't care enough. Good thing they can't get what they want, because if it were that easy to de-list a site without having any back end access to it,  then competitors would be doing it to each other non-stop.

If they refuse to make contact then they get to have everything working against them. If you can make contact, then the action items Matt suggested are the next steps.

Good luck with them as a client