Low-cost active stereo cameras are widely deployed on unmanned aerial vehicles, ground support vehicles, and outdoor machinery for obstacle perception, yet their region-of-interest (ROI)-level distance estimates suffer from systematic positive bias caused by sparse stereo matching, background pixel bleed within bounding boxes, and quadratic disparity-to-depth error propagation. We formulate ROI-level distance correction as an offline residual learning problem in which light detection and ranging (LiDAR) provides front-surface supervision during training while only the stereo camera is retained at deployment. We propose the Geometry-aware Residual Transformer Network (GRT-Net), a residual corrector that fuses a depth-crop convolutional neural network branch encoding the spatial depth distribution with a feature-token Transformer branch integrating bounding-box geometry, depth statistics, appearance cues, and semantic class; gated pooling adaptively re-weights the two streams, and an aleatoric Gaussian negative log-likelihood uncertainty head outputs a per-ROI confidence estimate. On a held-out test set of 5,684 ROI samples from an agricultural ground platform, GRT-Net respectively reduced mean absolute error (MAE), root-mean-square error, and 95th-percentile absolute error by 81.1, 75.6, and 63.0% relative to raw stereo depth, reaching an absolute MAE of 0.570 m, and by 54.4, 46.1, and 40.1% relative to the strongest multilayer perceptron residual baseline. Component-wise ablation and distance-bin analysis confirm that both branches and the uncertainty head contribute independently, with reliable correction sustained over the 0–30 m range. By confining LiDAR to an offline supervisory role and retaining only the low-cost active-stereo depth sensor at deployment, the method raises the ranging accuracy of a commodity stereo sensor toward LiDAR-grade levels, providing a sensor-level enhancement strategy for payload-constrained outdoor sensing platforms.