Google Tag Manager Expert needed

Our website is https://www.moknis.com/de/ ! So far so good... for a room booking we do have a 3rd Party Booking Engine: https://v4.ibe.dirs21.de/channels/mokniscom/?in_tab=true#start ! As far as I can see they addet our Google Manager Tag to this Booking Engine - Now I want to track if the guest booked a room (=last step of the booking engine)