Offline reinforcement learning (RL) often struggles with limited data. This work explores cross-domain offline RL where offline datasets (with possibly sufficient data) from another domain can be accessed to facilitate policy learning. However, the underlying environments of the two datasets may have dynamics mismatches, incurring inferior performance when simply merging the data of two domains. Existing methods mitigate this issue by training domain classifiers, using contrastive learning methods, etc. Nevertheless, they still rely on a large amount of target domain data to function well. Instead, we address this problem by establishing a concrete performance bound of a policy given datasets from two domains. Motivated by the theoretical insights, we propose to align transitions in the two datasets using optimal transport and selectively share source domain samples, without training any neural networks. This enables reliable data filtering even given a few target domain data. Additionally, we introduce a dataset regularization term that ensures the learned policy remains within the scope of the target domain dataset, preventing it from being biased towards the source domain data. Consequently, we propose the Optimal Transport Data Filtering (dubbed OTDF) method and examine its effectiveness by conducting extensive experiments across various dynamics shift conditions (e.g., gravity shift, morphology shift), given limited target domain data. It turns out that OTDF exhibits superior performance on many tasks and dataset qualities, often surpassing prior strong baselines by a large margin.