I help paid the phone bill various years for my mom and dad, but it's not in my name, so if I try to get the tax refund, will they just reject it or will it mess up my whole return?

If you file a return in your name and you claim the credit, you will get it.

I anticipate that the IRS will in no case challenge any credit request. It's a one-time credit for 2006 only. The maximum automatic credit is $60, with the average being $30. The IRS has bigger fish to fry than to try to track fraud on such cases.