If an owner’s Airbnb account was linked in Hospitable before you took over management, reviews from that account can appear on your site. There is no account-level filter for reviews in the Hospitable sync, but you have two options.
Hide reviews per home. Use the Review Visibility controls on the Reviews list in WordPress. Decide the date each home came under your management, then hide every review dated before that date. Hidden reviews stay hidden through future syncs and are dropped from the average and star counts.
Unlink the owner’s listing. Once the carried-over bookings from the owner’s Airbnb listing are complete, you can unlink that listing from the property in Hospitable. The next sync removes the reviews that no longer come through.