GateKD introduces a confidence-gated closed-loop reasoning distillation framework designed to transfer robust reasoning abilities from large language models into compact student models. Unlike conventional open-loop distillation approaches that assume uniformly reliable teacher supervision, GateKD dynamically modulates supervision quality through confidence-aware gating mechanisms. The framework integrates confidence-gated soft targets, gated hidden-state alignment, and reliability-filtered attention transfer to selectively preserve trustworthy reasoning trajectories while suppressing hallucinated or noisy intermediate representations. Extensive experiments on commonsense, logical, and symbolic reasoning benchmarks demonstrate that GateKD consistently improves reasoning fidelity, robustness, and low-resource generalization across T5 and Flan-T5 student models.