There is no cloth hat from the GBs.
There IS a cloth hat which resembles a sort of full plate helm, but I think it's from the Danonian Priests. Don't quote me.
The BGs drop two distinct leather hats which both looks like this. One with Friar skills, one with infil ones.
Yes, they are the tightest bastards EVER when it comes to dropping, matched only by Barfog mobs, Catacombs mobs and those new Priests of Awarn. :(
There is also a full set of af80 chain which drops from these bogeys. It looks FANTASTIC! Get it all.