Mixed Reality (MR) systems capture continuous video streams that expose bystanders' and collaborators' gait patterns -- a biometric revealing sensitive attributes including age, gender, and health conditions. We show that video-based gait profiling achieves 78\% accuracy (15.6$\times$ random chance) on unprotected MR feeds, motivating \textbf{GaitGuard}, a real-time defense operating on a companion mobile device. GaitGuard introduces \textbf{GaitExtract}, an automated gait feature extraction pipeline adapted from clinical analysis for egocentric MR perspectives. Through systematic evaluation of 233 mitigation configurations, we characterize privacy-utility-performance trade-offs. A key insight is that gait features derive primarily from transient events (heel strikes, toe-offs). We exploit this temporal sparsity through adaptive mitigation that selectively processes only gait-critical frames, achieving a 68\% reduction in profiling accuracy while preserving visual quality (SSIM: 0.97) at 29~FPS. \textbf{GaitGuard} scales to 10 simultaneous users with under 10ms latency. A qualitative study of 20-participants confirms that the users preferred a solution such as \textbf{GaitGuard} which provides privacy guarantees.