Data silos and the Matthew Effect in consortium blockchains lead to inadequate protection against malicious behaviors by traditional cross-chain auditing mechanisms, with high-reputation nodes monopolizing auditing opportunities. This paper proposes Rebel, a reputation-driven cross-chain auditing framework. The framework achieves privacy-preserving verification through decentralized identity and zero-knowledge proofs, employs a probabilistic node election mechanism to balance reputation and fairness, and designs a tax-based reputation pool management model to dynamically incentivize honest behavior. Experimental results demonstrate that Rebel effectively suppresses malicious behavior, achieves fair reputation distribution, and reduces cross-chain auditing latency by up to 90% in high-latency scenarios.