Unmanned aerial vehicles (UAVs) are envisioned to be extensively employed for assisting wireless communications in the Internet of Things (IoT). On the other hand, terahertz (THz) enabled intelligent reflecting surface (IRS) is expected to be one of the core enabling technologies for forthcoming beyond-5G wireless communications that promise a broad range of data-demand applications. In this paper, we propose a UAV-mounted IRS (UIRS) communication system over THz bands for confidential data dissemination from an access point (AP) towards multiple ground user equipments (UEs) in IoT networks. Specifically, the AP intends to send data to the scheduled UE, while unscheduled UEs may behave as potential adversaries. To protect information messages from the privacy preservation perspective, we aim to devise an energy-efficient multi-UAV covert communication scheme, where the UIRS is for reliable data transmissions, and an extra UAV is utilized as an aerial cooperative jammer, opportunistically generating artificial noise (AN) to degrade unscheduled UEs detection, leading to communication covertness improvement. This poses a novel max-min optimization problem in terms of minimum average energy efficiency (mAEE), aiming to improve covert throughput and reduce UAVs’ propulsion energy consumption, subject to satisfying some practical constraints such as the covertness requirements for which we obtain analytical expressions. Since the optimization problem is non-convex, we tackle it via the block successive convex approximation (BSCA) approach to iteratively solve a sequence of approximated convex sub-problems, designing the binary user scheduling, AP’s power allocation, maximum AN jamming power, IRS beamforming, and both UAVs’ trajectory and velocity planning. Finally, we present a low-complex overall algorithm for system performance enhancement with complexity and convergence analysis. Numerical results are provided to verify the analysis and demonstrate significant outperformance of our design over other existing benchmark schemes concerning the mAEE performance.