Many critical UAV (Unmanned Aerial Vehicle) applications, such as military and infrastructure inspection, offload the detection of video frames captured at each UAV to an edge server, and then feedback next actions based on detection results to the UAV. Apparently, the response time, which is from the capture of a video frame to the receipt of the corresponding feedback at the UAV, needs to be as low as possible so that the UAV can be agile to take actions guided by the edge server. However, we experimentally discover that conventional video streaming methods that do not downgrade frame quality to hurt detection accuracy may lead to either long response time or very small processed FPS (Frame Per Second), which may cause missing information. We then propose a congestion-avoidance adaptation (CAA) method for the UAV video frame delivery to minimize the response time while maximizing the processed FPS. We prototype the CAA on a UAV platform; the evaluation result confirms its effectiveness by showing that it can keep response times low while maintaining high processed FPS.