you hand them in at the guild unless otherwise prompted
Viewing post in Post bugs here (version 1.31 onwards)
Right, after running everywhere and talking to everyone in order to find the person who requested these leaves, I ended up handing the quest at the adventurer guild clerk and it appeared it was the guild themselves who requested this quest.
I still think you should mention it in the quest scroll description though, "deliver 16 medic leaves to the adventurer guild" is a simple line which could spare some troubles.