You do not need to remove the seatbelt although to install it you need to remove and then reinstall the bolt that holds the rear seatbelts to your c-pillars.

However with a c-pillar bar there people are not going to want to sit in the rear seats so removing the seatbelts could be some added weight savings albeit a very small savings that may only compensate for the added weight of the bar. I will probably remove them myself when I put the bar there since people do not sit in my rear at all.