Hello.
The Booking Manager plugin can import only the events/bookings that exists in the external .ics feed.
You need to be sure that booked and closed days are stored as events in the .ics feed, that generate that 3rd party service. So better to contact this 3rd party service about how to include the closed days in the .ics feed that generate this 3rd party service.
You can check what events exists in the .ics feed, by using the listing events shortcode from the Booking Manager plugin, or for example by testing that .ics feed in external validators, like this one: https://icalvalidator.com/index.html
Kind Regards.