actually... they don't.
(have the patches, that is.)
if you look at the new gof site... www.gobletoffire.com
... it shows the gang in their scarves (which makes me soooooo happy!) and there is no patch.
i knitted a poa/gof style scarf in gryffindor colors for the 6th book release... (i didn't wear robes because i live in az, plus the knitting took up a good chunk of my time!) i modified the atypically.knit pattern into 1x1 ribbing. (plus i knit on size 15s!!! i am a tight knitter)
many people wondered if i bought the scarf... then i told them the answer by pulling out my knitting! (i was making a go-go garter scarf from snb for a friend)
i even had a girl try to commission me to make her a scarf... but i couldn't. (i barely finished my own... i was weaving in my numerous ends and putting on fringe that day at work!)
the best part about the scarf is that it doubles as a late season football scarf for arizona state university (where i go...)!!!!! so a colorblock scarf would be a bit more harry potterish, but at the same time... total sun devil pride...