What you see here is the official "badge" of the Sooner family of Rafferty, a kerchief of a unique and particular design and color.
Each Sooner family has there own particular kerchief design--the fact that some of the non-turquoise kerchiefs seen in Chapter 7 : Scene 5 have no design means I'm still working out what they are.
Naturally I had to figure out the design of Mare's family, the Raffertys, up front. I derived the Rafferty design from an old Coat of Arms of Rafferty:
Rank and place are indicated by the color variations. In the example below, the color combination on the left indicate the wearer is a guest of the Raffertys or as-good-as-family. This is the variant that Griffen and Molly are seen wearing; they are under the Rafferty aegis and part of the same contract.
The variation on the right indicates a boss or chief of the family. You seen the current family matriarch, Mare's mother wearing this in the third panel of page 27. Mare, as heir apparent, also wears this variation, as do several other higher ups in the family. The high muckety-muck has no other distinguishing badge, you just know who they are.