I concur that it is a club, specifically a rifle club; hence the last two letters R.C. and the two crossed long arms. That leaves us with the M.M. and I doubt whether "Mounted" was one of the words as "mounted" when linked with the firearms and the military implies "mounted rifles" and as a military unit, they would not be a club. It appears that the long arms are muzzle loaders but again, I doubt if "muzzle" is either one of the words as it would be in conflict with the "rifle club"
I have googled NZ towns and perused A.W.Reid's, "Place Names Of New Zealand" but failed to find any locality which I could expect to be M.M.
Conclusion a rifle club badge, (as the OP described it as a badge") but not for a New Zealand club.
It would be interesting to see the reverse as there may be a makers name. What is puzzling is that the base circle, long arms and "foliage" appear to be a stamping, but the letters MMRC are an engraving. Possibly a modification of a military button that is a one off jewellers handiwork, not a badge maker's product, which is why I would like to see the reverse..
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