Often this is not a specific visible photo edit you can track. Lightroom’s Facebook Publish Service has been known to incorrectly flag images as modified, including after re-authenticating Facebook or changing publish-service settings. Changes on Facebook’s side can also create a mismatch that Lightroom interprets as needing a republish.

Other things that may trigger republish include metadata-related changes such as renaming keywords in Lightroom’s keyword list, and possibly moving photos to a different folder.

You can check the photo’s History panel for develop changes, but that won’t necessarily reveal publish-service or external sync issues. In practice, there isn’t a reliable built-in audit trail that tells you exactly which parameter caused the Facebook publish status to change. So if the image looks unchanged, the republish flag may simply be due to a publish-service inconsistency or bug rather than an actual edit.