This paper studies the problem of securing task offloading transmissions from ground users against ground eavesdropping threats. Our study introduces a reconfigurable intelligent surface (RIS)-aided unmanned aerial vehicle (UAV)-mobile edge computing (MEC) scheme to enhance the secure task offloading while minimizing the energy consumption of the UAV subject to task completion constraints. Leveraging a data-driven approach, we propose a comprehensive optimization strategy that jointly optimizes the aerial MEC (AMEC)'s trajectory, task offloading partitioning, UE transmission scheduling, and RIS phase shifts. Our objective centers on optimizing the secrecy energy efficiency (SEE) of UE task offloading transmissions while preserving the AMEC's energy resources and meeting the task completion time requirements. Numerical results show that the proposed solution can effectively safeguard legitimate task offloading transmissions while preserving AMEC energy.