Remote multimodal models offer strong numerical reasoning capabilities over charts and speech, but sending private inputs risks exposing sensitive content. Text-only sanitization cannot directly satisfy fixed media interfaces, while identity anonymization leaves the underlying task content exposed.

We introduce ReCast, an agentic plug-in framework that replaces source-specific content while preserving task-relevant relations and the required input modality. ReCast locally converts inputs into a shared textual evidence-query record, jointly rewrites entities and topics with a distilled 4B model, and substitutes values through a locally invertible, role-aware numerical map.

A reconstruction agent generates and validates the required media from the protected record. The remote solver returns a program whose protected operands are restored locally before execution.

On 4,000 held-out ChartQA and NMSQA examples, ReCast achieves 75.10% accuracy, retaining 92.43% of unprotected remote accuracy, while a model-based audit flags source-content leakage in 7.95% of solver-bound requests. It outperforms all evaluated local baselines, preserving the benefit of remote reasoning while reducing source-content exposure under existing media interfaces.