We consider a multi-pair two-way amplify-and-forward massive multi-input multi-output (MIMO) hybrid relay with MIMO user-pairs. We employ block-diagonalization-based digital baseband processing at the hybrid relay to cancel the inter user-pair interference, and equal-gain-combining-based radio-frequency (RF) processing to maximize the beamforming gain. We then construct digital relay precoder and the user precoder/decoders using generalized singular value decomposition (GSVD). We also optimize the following for the proposed GSVD transceiver. First, the network transmit power subject to per-stream quality-of-service (QoS) constraints. Second, rate of the transmit stream with the worst signal-to-noise ratio. Finally, sum-rate subject to the per-stream QoS constraints. We numerically show that the proposed hybrid relay has only marginally inferior performance than a full RF chain relay for the three optimization metrics. We also demonstrate the efficacy of the proposed GSVD design over another state-of-the-art transceiver design.