I have heard in the past that pressing 1 can be dangerous. Many hears ago, I was told that doing that will sometimes allow the person(s) calling to be able to call all over the world and charge them to your number. I don't know whether that is truth or fiction but, in any case, I will not take that chance.
I, too, have registered with the Federal Do Not Call list but the rub there is that you have to report for each number the name of the company, the telephone number, the date and time called. Since that probably needs to be done 2 or 3 times a day, the Federal Do Not Call law is useless.
I just called the number back and got the same message about this being "Ann" and it lets you press 1 to not participate in any future surveys. I hit it and they said they'd remove my number. I guess I'll have to wait and see... They've already called me three times now.
NEVER press "1" to be removed from their list. It just confirms that you have a working, live number that they can call repeatedly. They are already in violation of the Do Not Call list, so why should they honor a request to remove your number? Be smart, people.
Do not call them back. Do not answer their calls. Do not give them ANY credit card info. Report them to: https://complaints.donotcall.gov/complaint/complaintcheck.aspx