The graph linear canonical transform (GLCT)-based filtering methods often optimize transform parameters and filters separately, which results in high computational costs and limited stability. To address this issue, this paper proposes a trainable joint optimization framework that combines GLCT parameters and Wiener filtering into an end-to-end learning process, allowing for synergistic optimization between transform domain construction and filtering operations. The proposed method not only eliminates the cumbersome grid search required by traditional strategies but also significantly enhances the flexibility and training stability of the filtering system. Experimental results on real-world graph data show the proposed method outperforms existing methods in denoising tasks, featuring superior denoising performance, higher robustness and lower computational complexity.