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As valuable as the Internet of Things (IoT) has been to explore and monitor the land surface of the earth, the Internet of Underwater Things (IoUT) has been crucial to the investigation of the underwater environment. Due to the unique characteristics of the IoUT, such as long propagation delays, high bit error rates, and limited bandwidth, acoustic sensors that use sound waves are preferred for deployment. Consequently, it is difficult to apply the medium access control (MAC) protocol designed for the IoT sensors that use radio frequencies (RFs) in the IoUT. Particularly for densely populated sensor networks, the challenging and dynamic underwater environment leads to the loss of control and data packets, resulting in energy waste and unreliable connections. In addition to a sensor being constrained by energy, replacing its battery is infeasible. Therefore, packet loss and energy conservation should be handled at the MAC layer in order to improve the throughput and longevity of the network. In this paper, we propose a REceiver-Initiated MAC based on Energy-efficient Duty cycling called REMEDY-MAC. Using autonomous underwater vehicles (AUV) for data collection, REMEDY allows a group of nodes to conserve energy by announcing the duty cycling schedule until an AUV arrives at a certain location. Once an AUV reaches a location, it receives data according to a pre-established schedule managed by the active sender node and moves to the next set of nodes after completion of its tasks. The simulation results indicate that the proposed REMEDY protocol significantly outperforms other MAC schemes with respect to network parameters such as energy efficiency.