In a esophagogastric junction biopsy, what does hyperplastic esophageal squamous mucosa with rare intraepithelial eosinophil mean?

Not much. This is a benign diagnosis. If there were more eosinophils, we'd be more confident that reflux is present. Hyperplasia doesn't really mean much here. The key is what the biopsy report doesn't mention -- there's evidently no cancer, no severe inflammation or tissue damage. This will be correlated with the other information and a plan implemented.