Unmanned Aerial Vehicle (UAV) has been widely applied in many domains. But the computation and energy resource limitation severely hinders its development and application. Mobile Edge Computing (MEC) emerges as a promising platform to process the tasks offloaded from the UAVs to effectively improve the Quality-of-Service (QoS). To this vision, it is first required that the edge servers must be deployed with the needed service to handle the offloaded task. Fortunately, by exploring cloud native computing technology, it is possible to deploy container-based microservice to MEC in a prompt way. In this case, it raises the task scheduling problem on whether to deploy a new service or to utilize an existing service to balance the overhead between data transmission and the microservice deployment (i.e., container image pulling) for overall task completion time minimization. In this paper, the problem is first formulated in Integer Linear Programming (ILP) form, and proved to be NP-hard. We further propose an incentive-based request scheduling algorithm. Experiments based on track-driven simulations show that the total completion time for all tasks is reduced by 21.37% compared to the state-of-the-art solution.