Existing summarizers for memory systems are typically optimized for human-facing criteria such as faithfulness, which misaligns with their true objective: preserving the evidence needed to support future queries. We show that conditioning summarization on query-answer pairs substantially improves answer quality, and that this utility-aware behavior is transferable across queries. Motivated by these findings, we propose MemSuit, a self-distillation framework in which a teacher summarizer, conditioned on observed query-answer pairs, produces utility-aware memory entries that a student learns to reproduce from the raw conversation alone. To prevent collateral erasure where conditioning on a single query-answer pair discards evidence relevant to other plausible queries, the teacher decomposes each block into multiple self-contained entries that preserve distinct query-relevant facets as independently retrievable units. To align the retriever with the compact, fact-dense style of teacher entries, we further fine-tune the embedding model with a contrastive objective supervised by teacher entries. Across a diverse suite of conversational query types, MemSuit consistently outperforms state-of-the-art baselines, confirming the value of grounding memory in downstream utility.

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