LLM agent distillation transfers agentic capabilities by training student models on full teacher trajectories that contain both thoughts and actions. This work investigates how essential thought supervision is for the final action performance. We independently perturb teacher thoughts and actions during distillation to isolate their effects. Across several widely used agent benchmarks and various model scales, the results show that discarding teacher thoughts has negligible impact on student performance. The only scenario where thought supervision matters is when the information encoded in the thought is not reflected in the corresponding action during training. By pinpointing such discrepant cases, we challenge the prevailing practice of always distilling complete teacher trajectories for LLM agents and suggest that, when the action already conveys the necessary information, thought supervision can be omitted to improve efficiency.\n\nReview: The paper offers a thorough empirical analysis of the role of thought supervision, opening up more efficient strategies for future agent distillation.