In order for the plugin to be able to filter by a date, a post meta field should exist on each post, that needs filtering. This field has to contain a single date, of MySQL datetime or UNIX Timestamp number data type. These data types are commonly used for date storage. It is very likely, that the calendar already uses that.
Depending on the exact storage, data type and processing method, the calendar data has to be migrated as post meta of either of these types – so that there is a direct connection between posts and the metadata. There is my previous concern, that there might be a possibility for a 1 -> N connection between posts and dates, meaning that each post type could be assigned multiple reservation dates at different times. In that case, the date has to be stored in some sort of a complex array structure – which is no longer a single date field, and cannot be used for filtering, even if it was a post meta (as the field type is no longer a date, but a serialized object/array)
Unfortunatelys there is no exact answer on how to do that, as one has to programatically understand how exactly the calendar plugin works, how it manipulates the data.