An apparently-obsolete British idiom, meaning »a brawl, a fight«, particularly among somewhat genteel people who are meant to hold themselves above such crude things as fisticuffs. The idea is that when you punch a be-wiggèd man in the face, the first thing that happens is that his wig flies off and lands in the grass; besides being fairly typical of what Chesterton calls the theological joke, this rather conclusively dates the saying, to the late 17th or the 18th century.
Various unreliable sources allege that the idiom is originally Irish and refers specifically to »The Green« outside the Houses of Parliament in Dublin, but this explanation reeks of folk etymology to me; this type of overprecision is almost always the result of a fevered local imagination, and only in a few surprising cases true. I daresay it's far more likely that the image of a distinguished man having his wig knocked off has a universal appeal to all that is happy and delighted in Man.
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