Mobile relaying is envisioned as a promising technology to alleviate the masking effect in satellite links. Nevertheless, due to the mobility and limited communication range, the network topology in mobile relay networks becomes highly dynamic and time-varying, resulting in increased difficulty of network optimization. This letter investigates unmanned aerial vehicles (UAVs) aided hybrid satellite-terrestrial network, where UAVs are served as mobile relay base stations to assist the communication between the satellite and ground users. We aim to maximize the number of served users by optimizing UAV trajectory and user link selection. To solve the formulated mixed-integer and non-convex optimization problem, we first find the optimal link selection via a designed graph neural network (GNN), and then adjust the UAV locations by using model-free reinforcement learning (RL), alternately. Numerical results demonstrate that our proposed scheme is superior to the state-of-the-art RL algorithms.