Prevent duplicate sites from using my Dropbox

I set up a website for a client of mine a couple of years back and I always use Updraft for backups, and I connect my Dropbox account for automated backups. Which works great. Thank you.

Here’s the problem. My client decided to get someone to duplicate the site I built onto another domain, one which I have no control of. They exported the WordPress database from the site I set up, along with the Updraft settings, and my Dropbox connection. Their duplicate site is now backing up to my Dropbox account and I can’t seem to stop it.

To make matters worse, their duplicate site seems to have been hacked and all kinds of crazy subdomains are popping up. So now I’ve got multiple sites which I have no control of all backing up to my Dropbox.

Is there a way to block access of these domains from accessing using my updraft-dropbox connection? If not then I may have to block updraft from my Dropbox account entirely and find a new solution.