Large language models rely on context‑rich instructions for everyday tasks, which inevitably expose user‑sensitive data. Existing privacy methods often apply context‑agnostic static rules, causing severe utility loss. This work conducts a systematic analysis of the privacy‑utility trade‑off and identifies three mechanisms. First, context‑dependent utility shows that data value shifts from critical constraints to dispensable noise according to user intent, indicating when to sanitize. Second, strategic adaptation states that the sanitization method—removal or replacement—depends on whether the task prioritizes factual integrity or structural coherence. Third, combinatorial interplay reveals that attributes form a semantic web with synergistic dependencies or antagonistic redundancies. Guided by these insights, we propose an intent‑driven local protection framework. By distilling a lightweight model Veilmind‑4B to orchestrate a dynamic extraction‑sanitization‑restoration pipeline, we achieve a low‑leakage privacy point while preserving substantially higher response utility than prior baselines, moving the trade‑off toward the Pareto frontier. Review