What phone make and model number? There's both. 

I'm not sure what phone my mother has now, but she was looking to get a AT&T phone for her home. When she had the hearing impaired system put in she was told that she had to have the internet for it to work. She has a AT&T Dect 6.0 phone.

You best bet is to search the internet for caption phones, like I said there's both, those that require Internet and those that don't. The ones that don't there's an 800 number that callers call to get connected to the caption agent. There's many models of Dect phones, I don't think they make a caption phone, but I could be wrong.