Data integrity verification in geographically distributed edge systems remains a critical unsolved challenge. While centralized verification introduces bottlenecks and single points of failure, existing decentralized alternatives suffer from inefficiency due to their lack of batch verification capabilities. This limitation leads to prohibitive communication and computational overheads that scale poorly as data volume grows. This paper introduces EdgeBatch, the first decentralized protocol designed for efficient batch integrity verification, reducing communication rounds from$\mathcal {O}(n)$to$\mathcal {O}(1)$a small, constant number. At its core is a reputation-aware Combination Selection Algorithm (CSA), a polynomial-time heuristic that identifies near-optimal peer server combinations, balancing verifier group size against servers' historical trustworthiness through intelligent pruning strategies. This process is orchestrated through distributed ledger technology and smart contracts, ensuring a secure, transparent, and trustless verification environment. The protocol's design is underpinned by rigorous theoretical analysis, including formal proofs of security and correctness, and a probabilistic model for optimizing key system parameters. Extensive simulations show that EdgeBatch drastically outperforms state-of-the-art methods; it improves computational efficiency by an average of 518.60× over EdgeWatch and 1030.93× over CooperEDI, while also reducing communication overhead by 296.68× and 62.66×, respectively. A concluding ablation study confirms the vital role of our reputation mechanism, demonstrating it reduces the required verification rounds by 73% and is the key to the protocol's efficiency.