What kind of scarf are they wearing?

It's a special kind of scarf for denoting the exploration teams in their guild! (The story took place way after the event of EoS and after they left Wigglytuff's)
Every exploration team member there got a matching pair of scarves and a letter pin.

Functionality-wise it's probably identical to one of the stat scarves from the game, with the most prominent stat one being boosted.
(So in his case would be Sp.Atk, for example)

Oooooh! I think it's pretty cool! Eye-catching colors too! And the badge is a nice touch, just like my scarf! 👍

So handsome!