In this paper, the Relative Pose based Redundancy Removal (RPRR) scheme is presented, which has been designed for mobile RGB-D sensor networks operating under bandwidth-constrained operational scenarios. The scheme considers a multiview scenario in which pairs of sensors observe the same scene from different viewpoints, and detect the redundant visual and depth information to prevent their transmission leading to a significant improvement in wireless channel usage efficiency and power savings. We envisage applications in which the environment is static, and rapid 3D mapping of an enclosed area of interest is required, such as disaster recovery and support operations after earthquakes or industrial accidents. Experimental results show that wireless channel utilization is improved by 250% and battery consumption is halved when the RPRR scheme is used instead of sending the sensor images independently.