This grenade - the very example - has cropped up before:
https://www.bocn.co.uk/threads/mills-grenade-new-zealand-experimental.107968/
The link includes a further link that discusses possible reasons for the development, and shows a couple of other examples:
https://www.bocn.co.uk/threads/experimental-mills-grenade.98190/
WWII NZ munitions files mention a "Grenade Thrower, Local Pattern", for which a provisional order of 5,000 units was suggested for defence of the NZ home islands. In the event NZ manufacture of the No.1 discharger cup made the grenade thrower superfluous and it did not progress to production. Some prototypes were made and tested, so the question arises as to whether the modified No.36 with dual bands was a trial round?
Without details of what the grenade thrower looked like or how it operated there is no definitive answer - but the WWI-era Burn Gun, which could launch a Mills bomb, was invented by Lt Robert Burn, a Kiwi engineer who returned to New Zealand after the war. Burn was also the designer of the No.1 (S&B) discharger cup, and what with the Garland mortar, the New Zealanders had form for making bomb projectors with novel ammunition.
Attached image includes mention (fourth item) of the Hand Grenade Thrower, local pattern - NZ, 5000.
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