Google Tag Manager
Under 'Setup -> Booking site' you will find an input for entering your GTM ID.
Track conversions with GTM
When a booking is completed MakePlans will trigger the following event: 'booking_completed'.
You can then create a new trigger in your GTM workspace. This trigger should be of type "Custom Event" and you should filter so the trigger only occurs for Event equals 'booking_completed'. You can then use this trigger for the appropriate tag for a conversion.