Pathology foundation models (PFMs) achieve strong performance on diverse histopathology tasks, but their sensitivity to hospital-specific domain shifts remains underexplored. We systematically evaluate state-of-the-art PFMs on TCGA patch-level datasets and introduce a lightweight adversarial adaptor to remove hospital-related domain information from latent representations. Experiments show that, while disease classification accuracy is largely maintained, the adaptor effectively reduces hospital-specific bias, as confirmed by t-SNE visualizations. Our study establishes a benchmark for assessing cross-hospital robustness in PFMs and provides a practical strategy for enhancing generalization under heterogeneous clinical settings. Our code is available at https://github.com/MengRes/pfm_domain_bias.