Retrieving a target from clutter requires deciding whether to grasp the target, remove a blocker, or defer. Existing methods typically commit to a single obstruction graph or removal strategy, ignoring uncertainty across alternative scene interpretations. They also rely on miscalibrated vision-language model (VLM) predictions and can produce pairwise obstruction relations that are jointly inconsistent. Moreover, current approximations provide no guarantees about the impact of discarded hypotheses on the final decision. We propose CPOR-Grasp, a calibrated probabilistic obstruction-reasoning framework that propagates uncertainty from pairwise evidence to action decisions. CPOR-Grasp calibrates and fuses VLM, depth, and amodal-mask cues to estimate obstruction probabilities, induces a distribution over valid obstruction graphs, and marginalizes over these graphs to compute the likelihood that the target is accessible or that a given blocker should be removed. To make inference tractable, it retains only the highest-probability graphs and derives a total-variation bound on the discarded probability mass, enabling certified decisions, adaptive stopping, and principled deferral. On synthetic and real UNOBench scenes, CPOR-Grasp outperforms state-of-the-art baselines. Calibration error decreases from 0.1416 to 0.0185 on the Gemini Robotics backbone, while graph truncation matches exact inference on 99.74\% of decisions using 56 times fewer graphs. In real-world experiments, CPOR-Grasp achieves a 77.8\% average success rate, surpassing SOTA baselines.

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