In this study, we developed a novel registration method that distills knowledge from a teacher model into a compact student model, guided by weak supervision from landmark annotations. We demonstrated that our method significantly reduces inference time while achieving comparable artifact reduction on dual-energy X-ray images to commonly used, more compute-intensive unsupervised methods. A limitation of our study is the small dataset size due to the labor-intensive manual annotations. However, we believe our findings are scalable to larger datasets. Future work would involve the evaluation of our method as part of a clinical study.