It will not affect your service other than the nag message. When you run the phone connection test, does it work? Can you retrieve the list of dialin numbers for your area?
You could just disconnect the phone line and ignore it. The one side-effect of this is that you will not get any software updates installed.
My guess is that the problem is in your phone line and not the TiVo. What kind of phone service do you have? (Plain Old Telephone Service, VoIP, cable company phone, something else?)