Large language models (LLMs) have enabled powerful software engineering (SE) agents capable of navigating complex codebases and resolving real-world issues. However, these agents remain fundamentally episodic: they fail to retain, refine, and reuse experiences across tasks, repeatedly reconstructing context from scratch and reproducing similar mistakes. Even with memory support, they offer no remedy for the absence of a principled, task-agnostic \textit{memory utility}, making them difficult to evaluate rigorously or generalize across agents and settings. To tackle these limitations, we introduce MemOp, a closed-loop framework for memory augmentation in SE agents. MemOp grounds memory utility in \textit{validated downstream impact}, establishing utility as both a task-agnostic \textbf{evaluation benchmark} and an annotation-free \textbf{optimization signal}. Evaluating MemOp across four benchmarks, three programming languages, and two SE agents, under complementary \textit{single-episode} and \textit{cross-episode} memory augmentation, results demonstrate the \textbf{effectiveness} of MemOp, achieving absolute gains of up to $\uparrow5.25\%$ in success rate and $\uparrow4.63\%$ in resolve efficiency, while notably reducing deployment cost by $\geq10.33\%$. MemOp further exhibits \textbf{generalizability} across SE agents, memory backbones, and optimization algorithms, together with \textbf{transferability} of MemOp-trained memory model to unseen programming languages and SE activities. Our project page: https://xhguo7.github.io/MemOp/.

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