Unmanned aerial vehicles (UAVs) are envisioned to be extensively employed for assisting wireless communications in Internet of Things (IoT) applications. 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 pose potential adversaries. To protect information messages and the privacy of the scheduled UE, 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 a cooperative jammer generating artificial noise (AN) to degrade unscheduled UEs detection. We then formulate a novel minimum average energy efficiency (mAEE) optimization problem, targetting to improve the covert throughput and reduce UAVs' propulsion energy consumption subject to the covertness requirement, which is determined analytically. 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 planning. Finally, we present a low-complex overall algorithm for system performance enhancement with complexity and convergence analysis. Numerical results are provided to verify our analysis and demonstrate significant outperformance of our design over other existing benchmark schemes.