Non-orthogonal multiple access (NOMA) enables the parallel offloading of multiuser tasks, effectively enhancing throughput and reducing latency. Backscatter communication, which passively reflects radio frequency (RF) signals, improves energy efficiency and extends the operational lifespan of terminal devices. Both technologies are pivotal for the next generation of wireless networks. However, there is little research focusing on optimizing the transmit power in backscatter-assisted NOMA-MEC systems from a green IoT perspective. In this paper, we aim to minimize the transmit energy consumption of a Hybrid Access Point (HAP) while ensuring task deadlines are met. We consider the integration of Backscatter Communication (BackCom) and Active Transmission (AT), and leverage NOMA technology and user cooperation to mitigate the double near-far effect. Specifically, we formulate a transmit energy consumption minimization problem, accounting for task deadline constraints, task offloading decisions, transmit power allocation, and energy constraints. To tackle the non-convex optimization problem, we employ variable substitution and convex optimization theory to transform the original non-convex problem into a convex one, which is then efficiently solved. We deduce the semi-closed form expression of the optimal solution and propose an energy-efficient algorithm to minimize the transmit power of the entire wireless powered MEC. Simulation results demonstrate that our proposed scheme significantly reduces the transmit power of the HAP compared to existing schemes, validating the effectiveness of our approach.This study provides valuable insights for the design of green IoT systems by optimizing the transmit power in NOMA-MEC networks.