Didn't answer. Reading the above, all I can say is that we can all hope the real CenturyLink (what a horrible name) is powerful enough and p*ssed enough to pursue these people.
It's a company called "CTS Communications" who is an "authorized representative" of CenturyLink --- in other words it's a SCAM... they are trying to get you to switch LL service to them.
They keep calling claiming they are with ceturylink and need to talk with the owner about the phone service. First giveaway it's fake, they would have the owners name when they call. Number blocked problem solved until they switch numbers again.