Intelligent education systems often collect exam sheets as in-the-wild photos. These photos often suffer from distortions and noise caused by handwriting and occlusions, collectively referred to as Real-World Degraded Exam Images (RDEI). Structure-preserving reconstruction is key to converting RDEI into structured assets for downstream educational applications. Existing Multimodal Large Language Models (MLLMs) often fail under RDEI, leading to disrupted structure and evidence-unsupported hallucinations. To tackle these challenges, we propose MessToClean, a backbone-agnostic, evidence-driven pipeline that treats off-the-shelf MLLMs as interchangeable components. By grounding extraction in pixel-aligned evidence and enforcing post-hoc consistency auditing on recovered structures, MessToClean mitigates unsupported hallucinations and enhances both controllability and structural fidelity in question-level reconstruction. We curate RDEI-Exam from our educational platforms and evaluate across 12 state-of-the-art MLLM backbones. Across these, MessToClean improves stem consistency by 1.01-3.18%, figure consistency by 0.50-49.16%, and refusal F1 by 1.06-10.88% across question types.