Unmanned aerial vehicles (UAVs) are widely used for surveillance in both civilian and military scenarios. The utilization of UAVs provides an opportunity for monitoring landslide-prone areas by automatically collecting geological information, thereby reducing the risks and the time required to be working in harsh environments. Due to the maximum travel time limit of UAVs and the geographical dispersion of landslide-prone areas, multiple UAVs are dispatched for surveillance tasks, and landslide-prone areas with high emergency priorities require mandatory visits. Here, we investigate a team orienteering problem with mandatory visits (TOPMV) for routing multi-UAVs to monitor scattered landslide-prone areas, with mandatory visits on those in poorly stable states. The proposed TOPMV aims to plan the optimal multi-UAV paths for maximizing the total amount of collected geological information. To solve the TOPMV with a realistic scale, we develop a large neighborhood search (LNS) algorithm embedding a neural network heuristic (NNH), in which the embedded NNH learns to perform adaptive destroy operators through a hierarchical recurrent graph convolutional network (HRGCN). We consider a real-world case study for monitoring of landslide-prone areas in three counties in southern Shaanxi Province, China. Finally, we test the proposed NNH on both small- and large-scale benchmark instances of the team orienteering problem. The experimental results demonstrate that our proposed NNH exhibits higher efficiency and provides better solution quality than state-of-the-art methods, especially in large-scale settings.