It's possible that it's a specific reference to a door:
* A door covered in green baize fabric: Green baize is a type of felt cloth that was historically used for covering surfaces like pool tables, card tables, and sometimes even doors. This could be a description of a particular door.
* A door associated with a specific location: It might be a name or nickname given to a specific door in a building or institution, perhaps referencing the green baize covering.
Without more context, it's difficult to determine the exact meaning of "green baize door."
If you can provide more information about where you encountered this phrase, I might be able to help you understand its meaning.