Behavior Foundation Models (BFMs) enable scalable imitation learning (IL) by pretraining task-agnostic representations that can be rapidly adapted to new tasks. However, existing BFMs assume fixed environment dynamics, limiting their robustness under real-world shifts such as changes in friction, actuation, or sensor noise. We address this by formulating BFM task-inference as a robust minimax optimization problem, enabling adaptation to worst-case dynamics perturbations without modifying pretraining. To the best of our knowledge, this is the first BFM-based framework that achieves robustness to dynamics shifts while relying solely on offline data from a single nominal environment. Our approach significantly outperforms standard BFM and robust offline IL baselines under dynamics shifts. These results demonstrate that robust policy can be achieved entirely at task-inference time, improving the practicality of BFMs in dynamic settings.