Most LiDAR odometry and SLAM systems construct maps in point clouds, which are discrete and sparse when zoomed in, making them not directly suitable for navigation. Mesh maps represent a dense and continuous map format with low memory consumption, which can approximate complex structures with simple elements, attracting significant attention of researchers in recent years. However, most implementations operate under a static environment assumption. In effect, moving objects cause ghosting, potentially degrading the quality of meshing. To address these issues, we propose a plug-and-play meshing module adapting to dynamic environments, which can easily integrate with various LiDAR odometry to generally improve the pose estimation accuracy of odometry. In our meshing module, a novel two-stage coarse-to-fine dynamic removal method is designed to effectively filter dynamic objects, generating consistent, accurate, and dense mesh maps. To our best know, this is the first mesh construction method with explicit dynamic removal. Additionally, conducive to Gaussian process in mesh construction, sliding window-based keyframe aggregation and adaptive downsampling strategies are used to ensure the uniformity of point cloud. We evaluate the localization and mapping accuracy on five publicly available datasets. Both qualitative and quantitative results demonstrate the superiority of our method compared with the state-of-the-art algorithms. The code and introduction video are publicly available at https://yaepiii.github.io/CAD-Mesher/.