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We introduce \\itermodelfull (\\itermodel), an inference-time method that leverages hallucination detectors to guide iterative summary revisions toward factual corrections. Building on this, we propose \\itermodel for Preference Learning (\\model), which converts detector-guided refinement trajectories into preference pairs for model finetuning. Extensive experiments show that our methods substantially reduce hallucinations for Llama and Gemma models in summarizing real-world clinical notes from \\MimicIV. For example, \\itermodel reduces 24\\% and \\model reduces 48\\% hallucinations in Llama-3.1-8B-Instruct. 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