When one finds oneself in a situation "south of the border" with a lady....and the "situation" is not a place you care to be. In other words, things are bad (ie. smell, presence of discharge, discolouration, etc.) - very bad. In such a case a "courtesy" lick is given to the area in question followed by a similar lick of the thumb and subsequent manual stimulation of the clitoris (w/ said thumb).
I started to go down on this chick and she was super hot." "However, the state of her genital region required the use of a courtesy lick.