The Grand Order of the Nght Owls is a made up order by René and Edith as a part of a coverup story. René himself is supposedly the Grand Master Big Hoot of this order.
The Resistance are planning to get the two British airman home by sending them off in a small airplane. To get it airborne they need to collect braces in order to make a rubber band to pull up the small airband. René is acting as a middleman to the Resistance to collect braces from people of Nouvion to create this rubber band.
In the episode Flight of Fancy, while talking to Captain Hans Geering and Colonel Von Strohm, René is out of the blue receiving a brace from one of his customers. Von Strohm acts very suspicious about this matter. To cover up the secret operation, René and Edith have to make a cover up story about a secret order called The Grand Order of the Night Owls. To be initiated in the order, members have to wear no braces for three weeks.
The name Edit
The reason why the order got its name 'Night Owls' is simply because owls doesnt wear braces, which is connected to the recruitment of new members.