The extender will only help with phone calls. It won't provide you with 4G service to use with your data. In which case my suggestion is to use a free app to make free phone calls over wi-fi; assuming you have a good wi-fi connection which is needed for an extender anyway.

Verizon will usually discount the extender for you if you've been complaining about lack of service for years and have opened a ticket for them to come out and investigate the towers.

I've had great success getting on Chat with them about lack of service. They sent someone out within 24 hours and they reported back to me what the issue was. How many service tickets have you opened?