This is one of the Lower Your Rate credit card companies. There is no number to press to have your phone line taken off their list. When you press "1" and ask to be removed, you are told that "they didn't call you, you pressed "1" to be connected to them."
The individual told me the name of the company was Credit Card Services, LLC located in Bridgeport, CT. He told me I could access them by calling the number on the back on any of my credit cards. Amazing, since my credit cards are from different providers.
There is no recourse for this because the No Call List is not enforced by anyone, and these companies seem to feel like they a) don't have to give you a way to get off their lists; b) by dialing "1' you called them, they didn't call you.
And then, they guy had the nerve to tell me they were a legitimate company. Unfortunately, even the definition of legitimate has changed.