Supply Chain
Not wishing to take the thread off into irrelevant territory, a point about supply of the Armies in the field is worth making to explain the presence of NZ, Australian, and South African No.36 and other munitions in the Mediterranean and ultimately mainland Europe. Essentially islands like Malta, Crete, etc. did not buy grenades from far flung corners of the globe as they saw fit, and neither were Commonwealth Divisions and Corps of the British Army equipped (other than by coincidence of what was held in ammunition depots) with grenades from their homelands.
Soon after the outbreak of WWII, the industrial capabilities of the Empire were organised by region, and in India the Eastern Group Supply Council swung into action. EGSUP, or more commonly called SUPEG, had overall responsibility for creating munitions industries in India, Union of SA, Australia and New Zealand. In a very simplified nutshell, munitions requirements desired from east and south of Suez were passed from the UK Ministry of Supply to SUPEG, which then dealt with the various industrial boards of the individual countries, who then sorted individual production contracts in their own countries. For No.36 there was one rolling contract letter from the MoS which periodically extended production runs.
For New Zealand, a first contract for 25,000 empty grenades, to be filled in Canada, was placed in May 1941. Thereafter, as New Zealand (a) proved it could make No.36 grenades and (b) got filling facilities established, the big contracts were put in place. The first, for 1 million "complete, filled" grenades, was dated 12 January 1942, and other orders in excess of 1 million followed in 1943 and 1944.
In 1942 completed orders were shipped to Durban, and then up the coast of East Africa, heading for either Egypt for the Western Desert theatre, or Bombay for Burma requirements - the Japanese being in the process of chasing the two British/Burmese divisions from Rangoon up to the NE Indian border. Indian production finally became sufficient for Burma campaign needs, but NZ grenades continued to Egypt for the fighting up to El Alamein, and after to the end of the Tunisian campaign. Thereafter supplies continued for the Sicilian and Italian campaigns. Briefly, wherever the supplies were disembarked from ships, they found their way to Army Base Depots, and ultimately passed on to Corps and Divisional ammunition dumps, where they were issued to Brigades and Battalions at the front.
2nd NZ Division fought in Italy, and from time to time some of their troops may have picked up NZ-made grenades from a Divisional dump, but if so it was more by luck than judgement. They were just as likely to pick up grenades made in Johannesburg or Manchester.