Visual search over high-resolution images requires a vision-language model (VLM) not only to determine where to inspect, but also whether another observation is warranted before committing to an answer. Existing prompting, demonstrations, and outcome-based reinforcement learning can encourage re-examination, yet do not directly supervise whether it is beneficial at a particular search state. We introduce ReSee, a benchmark of re-examination decisions comprising 3,227 visual-search trajectories and 8,827 explicit commit-or-re-examine decisions, with counterfactual adjudication that distinguishes states where additional inspection is warranted from those where commitment is preferable. Building on this formulation, we propose CARE (Counterfactual Advantage for Re-Examination), a decision-level reinforcement learning method that compares paired continuations under commit and re-examine verdicts from the same search state. Their cost-aware return difference estimates the counterfactual value of an additional observation and is assigned only to the corresponding verdict tokens, providing localized credit for whether search should continue. Experiments expose limited re-examination selectivity in existing VLMs and show that CARE significantly improves accuracy and decision selectivity over GRPO across two backbones, with higher accuracy and fewer visual requests on six unseen OOD benchmarks.

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