Recent GUI agents have made substantial progress in visual grounding and action prediction, yet they remain brittle in long-horizon tasks that require maintaining task state across many interface transitions. Existing agents typically rely on raw history replay or text-only memory, which either overwhelms the model with redundant screenshots or discards localized visual evidence needed for future decisions. To address these limitations, we introduce MementoGUI, a plug-in agentic memory framework that equips MLLM-based GUI agents with MementoCore, a learned controller for online memory selection, compression, and retrieval. Rather than treating interaction history as a fixed context, MementoGUI formulates long-horizon GUI control as an online memory-control problem: working memory selectively preserves task-relevant interface events with textual summaries and ROI-level visual evidence, while episodic memory retrieves reusable past trajectories through learned relevance selection. MementoCore modularizes memory control into specialized operators for step processing, memory compression, episodic writing, and episodic selection, enabling plug-in memory augmentation without finetuning the GUI agent backbone. We further develop a scalable data curation pipeline that converts computer-use trajectories into memory-controller training data, introduce MementoGUI-Bench for evaluating long-horizon decision-making in GUI agents, and design MLLM-based metrics for semantic action matching, task progress, and memory consistency. Experiments on GUI-Odyssey, MM-Mind2Web, and MementoGUI-Bench show that MementoGUI consistently improves GUI agents over no-history, history-replay, and text-only memory baselines, with larger MementoCore backbones further strengthening memory-augmented GUI control.