Does basic cable local TV service NEED a router that VERIZON is billing me?

[NYCgrandma]

I have FIOS Local TV Service since the beginning and my daughter recently found a router behind my TV, BUT I do NOT have internet service. Do I need this router for regular basic cable TV? One rep told me that it is supposed to give me better reception like an antenna BUT again, I do NOT have wifi. One rep told me something like I needed it for On Demand, but I do not even use it because I'm a senior citizen. I just watch basic channels and I HAD to get cable in the first place because the building I live in has bad reception so I basically had no choice. Can someone honestly tell me that I need the router that I have been paying the rental fee every month? Please help. I'm a senior citizen on limited income and I feel like they are not telling me the truth.

[Edg1]

It definitely doesn’t have anything to do with reception. It provides internet connection to your cable box so the  On demand and the TV Guide works. That part is true. 

You don’t need the router that they provided. You can have your daughter order one online. The Actiontec rev i will do what you need and it will avoid the rental fee every month.