As GUI agents increasingly rely on screenshots to perceive and operate digital environments, they may inadvertently expose sensitive information such as identities, accounts, locations, and behavioral traces. While existing benchmarks primarily focus on task completion, grounding, or defenses against third-party attacks, current visual privacy datasets remain largely restricted to static natural images, limiting their ability to capture the contextual dependence and task relevance of privacy risks in GUI task trajectories. To bridge this gap, we introduce \textbf{GUIGuard-Bench}, a first-step benchmark for studying privacy-preserving GUI agents in trajectory-based GUI workflows. GUIGuard-Bench contains 241 real GUI-agent trajectories with 4,080 screenshots across Android and PC environments. Each screenshot is annotated at the region level with privacy bounding boxes, semantic privacy categories, risk levels, and whether the private information is necessary for completing the task. Built on these annotations, GUIGuard-Bench supports three complementary evaluations: privacy recognition, offline planning fidelity under protected screenshots, and the utility impact of different protection strategies. Our results show that current models can often detect whether a screenshot contains private information, but they struggle with fine-grained localization, category recognition, risk assessment, and task-necessity judgment. We also find that closed-source models, exemplified by Claude Sonnet 4.6, can maintain largely consistent planner semantics in Android environments after privacy protection is applied. Our results highlight privacy recognition as a critical bottleneck for practical GUI agents. Project: https://futuresis.github.io/GUIGuard-page/