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.
I've received over a dozen calls from "Rachel" this year alone. Not to mention another half dozen with a slightly different spiel. I've reported every one to the FTC. Yes, robocalls are illegal. I've also filled a formal complaint about "Rachel" and the FTC with my Senator. Every time you get a call, file these complaints and keep a record to backup the complaints. BTW, if you have a Republican Representative (as I do) or Senator, don't bother to complain to them. Republicans are pro-business, even illegal business.
Well, I TOOK the call, pressed 1, spoke with the representative at length, and when I questioned the validity of the caller and asked him to bear with me and give me some proof of the organization through which they were calling, he put me on the line with his supervisor, who put my mind at ease. I GAVE my credit card number and last 4 of my social!!!! While she went on and on about this great program to lower all my interest rates, I went online and started searching, and found out I'm being scammed. NOW WHAT TO DO??? Called my credit card company and reported the card "lost or stolen." Hope that protects me.