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Multimodal perception systems for robotics and embodied AI often assume reliable RGB-D sensing, but in practice, depth is frequently missing, noisy, or corrupted. We thus present GeomPrompt, a lightweight cross-modal adaptation module that synthesizes a task-driven geometric prompt from RGB alone for the fourth channel of a frozen RGB-D semantic segmentation model, without depth supervision. We further introduce GeomPrompt-Recovery, an adaptation module that compensates for degraded depth by predicting the fourth channel correction relevant for the frozen segmenter. Both modules are trained solely with downstream segmentation supervision, enabling recovery of the geometric prior useful for segmentation, rather than estimating depth signals. On SUN RGB-D, GeomPrompt improves over RGB-only inference by +6.1 mIoU on DFormer and +3.0 mIoU on GeminiFusion, while remaining competitive with strong monocular depth estimators. For degraded depth, GeomPrompt-Recovery consistently improves robustness, yielding gains up to +3.6 mIoU under severe depth corruptions. GeomPrompt is also substantially more efficient than monocular depth baselines, reaching 7.8 ms latency versus 38.3 ms and 71.9 ms. These results suggest that task-driven geometric prompting is an efficient mechanism for cross-modal compensation under missing and degraded depth inputs in RGB-D perception.