File a fraud alert with the credit reporting agencies and also get your credit card number changed. I think these people are credit card thieves. Since they can spoof your phone number, they can call your credit card provider and make it look like the call is coming from your phone. I think all they need is the last four digits of your credit card to access your account. That is one racket, asking for your card number is another. If you reported your card stolen, they should not be able to do anything with it and hopefully they will get caught when they try to buy something with it.
My new approach is to pretend interest and, when they ask for my credit card information, tell them I have to go find the credit card. Then I let them sit and wait while I work on the computer or do something else. In a couple of cases (after they've waited several minutes) I tell them I am on the Do Not Call list and never had any interest in their so-called service.
Got the same call. Pressed 1 for an operator. She, I guess, said the name of the 'company' (I wasn't listening) and then asked if I had debt with a credit card. I said "Yeah, you called me and..." CLICK. They hung up before I even had the chance to ask to be taken off the list.