Geometric Foundation Models (GFMs) have recently advanced monocular SLAM by providing robust, calibration-free 3D priors. However, deploying these models on dense video streams introduces significant computational redundancy. Current GFM-based SLAM systems typically rely on post hoc keyframe selection. Because of this, they must perform expensive dense geometric decoding simply to determine whether a frame contains novel geometry, resulting in late rejection and wasted computation. To mitigate this inefficiency, we propose LeanGate, a lightweight feed-forward frame-gating network. LeanGate predicts a geometric utility score to assess a frame's mapping value prior to the heavy GFM feature extraction and matching stages. As a predictive plug-and-play module, our approach bypasses over 90% of redundant frames. Evaluations on standard SLAM benchmarks demonstrate that LeanGate reduces tracking FLOPs by more than 85% and achieves a 5x end-to-end throughput speedup. Furthermore, it maintains the tracking and mapping accuracy of dense baselines. Project page: https://lean-gate.github.io/