Large Language Model (LLM) agents are increasingly deployed under structured generation, where grammar constraints enforce output format at inference time. Whereas existing compression methods target unconstrained generation, we first identify a fundamental mismatch: under structured generation, grammar constraints reduce the model's output distribution to valid tokens, and the logits matter most at the small set of positions that decide the agent's action. Motivated by this finding, we propose SKIM (Selective Knowledge-Informed Masking), the first pruning and distillation framework for LLM agents under structured generation, with both stages guided by token role. SKIM partitions token positions into context, decision, and format categories, and this partition drives two complementary axes: (1) category-aware pruning saliency scores that preserve parameters most relevant for decision positions; and (2) an on-policy distillation objective that aligns student and teacher on valid tokens, paired with category-aware feature matching. We evaluate SKIM on tool-calling benchmarks and within multi-step agent loops, across multiple model scales and sparsity levels. SKIM consistently improves accuracy over baselines, with its superiority becoming most striking in high-sparsity regimes where conventional methods struggle, demonstrating the potential of category-aware compression for deployment-time grammar-constrained agents.

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