Automated evidence-based misinformation detection systems, which evaluate the veracity of short claims against evidence, lack comprehensive analysis of their adversarial vulnerabilities. Existing black-box text-based adversarial attacks are ill-suited for evidence-based misinformation detection systems, as these attacks primarily focus on token-level substitutions involving gradient or logit-based optimization strategies, which are incapable of fooling the multi-component nature of these detection systems. These systems incorporate both retrieval and claim-evidence comparison modules, which requires attacks to break the retrieval of evidence and/or the comparison module so that it draws incorrect inferences. We present CAMOUFLAGE, an iterative, LLM-driven approach that employs a two-agent system, a Prompt Optimization Agent and an Attacker Agent, to create adversarial claim rewritings that manipulate evidence retrieval and mislead claim-evidence comparison, effectively bypassing the system without altering the meaning of the claim. The Attacker Agent produces semantically equivalent rewrites that attempt to mislead detectors, while the Prompt Optimization Agent analyzes failed attack attempts and refines the prompt of the Attacker to guide subsequent rewrites. This enables larger structural and stylistic transformations of the text rather than token-level substitutions, adapting the magnitude of changes based on previous outcomes. Unlike existing approaches, CAMOUFLAGE optimizes its attack solely based on binary model decisions to guide its rewriting process, eliminating the need for classifier logits or extensive querying. We evaluate CAMOUFLAGE on four systems, including two recent academic systems and two real-world APIs, with an average attack success rate of 46.92\% while preserving textual coherence and semantic equivalence to the original claims.