Knowledge within large language models (LLMs) inevitably lags behind an evolving world, motivating knowledge editing methods that update facts without expensive retraining. In multi-hop knowledge editing, models must not only recall updated facts but also correctly propagate them through multi-step reasoning chains. However, most existing approaches rely on unidirectional, feed-forward pipelines, decomposing questions and retrieving edited facts in a rigid hop-wise sequence. This design is brittle: a minor retrieval error or logical mismatch at an early hop can become a silent failure that cascades to the final answer without an explicit recovery mechanism. To address this limitation, we propose Critic-Guided Multi-Agent Reasoning for Knowledge Editing (CARE), a framework for closed-loop post-edit reasoning. A Critic agent performs chain-level verification by checking both global coherence and step-wise correctness, and triggers bounded backtracking for iterative self-correction, while a Selector agent supplies high-fidelity, low-noise candidate pools from the edit store to enable effective revision. Experiments on MQuAKE-2002 and MQuAKE-hard demonstrate that CARE effectively mitigates error propagation, achieving a new state-of-the-art.