If your mother has caller id and she still doesn't know who it is, just have her pick the phone up and set it down. If the tv is on, that's fine, people are talking, that's fine. Just say nothing until the call is terminated on the other line. Also, you can answer the phone, and if they ask for your mother, have her say "hold on a minute please", and have her call out for her mother to answer the phone. This drives the solicitor nuts after a minute and they'll hang up. You can do or say anything you want. Eventually they will get tired of calling. The easiest thing to do is hook up the old answering machine. Voice mail if it's available too. There is no need for you mother to get harrassed. Just plain your game with them and YOU will be in control.
@Celestial again: The actual best thing is caller id. Your mother doesn't have to answer the phone at all. Just let it ring if it's not someone she wants to talk too. Take CONTROL!