The scarf quest unlocks a mask shop in Master Li's Woods, where you can get multiple masks for 2500 gralats each.
You need a BURGER before you start, so buy one from Burger Refuge. Now go to North Graal/MoD Town, and just follow the path straight north. Enter the cave and follow through the door (or small waterfall if you prefer), get in the water and swim to right into next room. You'll find a half-dead dude named Monty. Feed Monty your burger and he will give you CAT FOOD.
Now do an "unstuck me". From Sister Gertrude's, walk east to the outdoor bar called The Joint. Give your tasty cat food to Morris, whose kitty is stuck in the tree. He will use the cat food to lure Mr. Chunnitz down from the tree and will give you a RAG.
In MoD Town, theres a small shack between where Red Dragon Inn and Black Orchid were moved. Give the rag to Raphael. He will dust off his boxes and give you a MIRROR.
Now Unstick and make your way over to Chris Kill 'Em's (the mansion in the cave next to Angel Clan). In the bathroom, Undine, the self proclaimed Queen of Graal, will swap your mirror for a SHIRT.
Get on a horse, because now you gotta get to York Town. Enter the bar next to Alan who sells the phoenix. Present the shirt before Jackman, who will grant you with a lovely box of MATCHES.
Unstick and go to Sara Rei's house, where SNC Guild House used to be. Uh oh! The door's locked... but theres a crack in the roof. Jump off the side of the cliff to crash through poor Sara's roof. Your crash landing somehow manages to blow out Sara's candles and she gets ticked off at you. Give her the matches so she can relight the candles. She gives you a PAINT BRUSH.
Now go to where the old Master Li's Sparring Dojo USED to be. In the middle of the forest, there is a painter named Hyto. Surrender the paint brush and gain a BOOK.
Now head on to the Battle Arena's Library. There's a fellow there named Everest who has been searching for a particular book ever since the library opened. It just so happens you have the exact book he's looking for!*Now your new friend gives you FISHING LINE.
Now go see our old buddy Toll Guy at the south end of the bridge. He will tell you a long and very boring story. Basically he got bored with gambling with RPS, so he wants to take up the hobby of fishing. Fork over the string to him. Congratulations you won a SCARF.
After obtaining the scarf, a new shop will appear in the trees next to Hyto, our painting buddy in Master Li's Forest. Apparently, the shop owner was not ready to open... so you have to wait 30 minutes and come back. Why did you need a scarf for that? Don't ask me. However there are rumors that the quest is still incomplete and the scarf may be used in the future.
This quest Info was obtained from
http://graakass.wikia.com/wiki/Quests
I am too lazy to write all that