Reviews synced from your PMS show the text exactly as the guest wrote it on Airbnb or Booking.com.
Why edits do not stick. Your site overwrites review content on every sync, so any change you make to the text of a synced review is replaced on the next refresh.
What you can do. If a synced review should not appear on your site, hide it rather than editing it. Imported historical reviews that are not part of the PMS sync can be edited directly, because the sync does not touch them.