While large generative artificial intelligence (GenAI) models have achieved significant success, they also raise growing concerns about online information security due to their potential misuse for generating deceptive content. Out-of-context (OOC) multimodal misinformation detection, which often retrieves Web evidence to identify the repurposing of images in false contexts, faces the issue of reasoning over GenAI-polluted evidence to derive accurate predictions. Existing works simulate GenAI-powered pollution at the claim level with stylistic rewriting to conceal linguistic cues, and ignore evidence-level pollution for such information-seeking applications. In this work, we investigate how polluted evidence affects the performance of existing OOC detectors, revealing a performance degradation of more than 9 percentage points. We propose two strategies, cross-modal evidence reranking and cross-modal claim-evidence reasoning, to address the challenges posed by polluted evidence. Extensive experiments on two benchmark datasets show that these strategies can effectively enhance the robustness of existing out-of-context detectors amidst polluted evidence.