Proposes JitMem, an agentic memory system that defers curation from write time to read time: instead of distilling a fixed, query-independent summary immediately after a task, it retains raw trajectories and synthesizes a compact, task-adaptive payload only once the current query is known. Because the curator is trained on immediate task success rather than delayed utility signals, it avoids the long-horizon credit-assignment problem of write-time memory curators. Across ALFWorld, WebShop, and tau2-bench, JitMem outperforms no-memory agents and both heuristic and learned write-time memory baselines by 16.2, 16.3, and 3.9 absolute success-rate points respectively.