Maybe it didn't matter that much at the time when they refurbished them, but a year later in 1938 they had the stainless steel rim.
The Australians & Newzealanders had a raw edge in WW2, plus the BMB 1941 was raw edge, & then there is the BMB made 1953 Mk4 that was rimless.
Here's a couple of pics of the Mk1 & Mk2 chin strap lugs, both on a Mk1*.
Here are my British Mk.I*s.
A rimless FKS 104, with Mk.I lugs and chin-strap. It was issued to a sapper named Anderson, who has impressed his identity very clearly on both sides of the helmet brim. The Lining Mk.I is B.H.&G. LTD (Barrow, Hepburn & Gale Ltd.London) 1939.
A rimmed Mk.I body HS 33, the size 6 3/4 Lining Mk.I is Helmets Ltd.1937
Now this one is curious, as the stamp on the rim 289 ZD and its dimensions 313x288 indicate that it started life as a US-made M1917, but it has acquired a set of Mk.III lugs, a Mk.III chin-strap and a Mk.II Lining made by FFL in 1945. The colour and MP on the front are something I have not seen on a British helmet, but I assume it is a British conversion using an M1917 which possibly came to the UK with the first US contingents. I would welcome any enlightenment.
Nice Mk1*'s, I note the white M, which means the helmet has become magnetic.
I am not sure "become' is the right verb. The only part that is magnetic is the rim, which being the original mild-steel rim was always magnetic.
Now for something somewhat different, the Canadian equivalent of the Mk.I*, although I have never seen the term used in official Canadian documents. When the Canadian Department of National Defence issued its requirement to manufacture 25,000 Mk.II helmets in late January 1940, it also requested an additional 26,250 liners, chin-straps and lugs to re-fit existing stocks of Mk.I helmets.
Here are some examples. The first, stamped HS17 has the early pattern three piece chin-strap with the closed rectangular buckle (see Mark K's excellent photo essay on the Canadian Mk.II The Canadian Mk II and its components ) However, it was later in its career painted that shiny green that characterises virtually everything the Canadian Army owned in the 1950s, and the Lining is dated 1943.
This one, FS145 is a bit different, note the flat headed machine-rivets, not the usual domed type. It seems to have been stripped of its fittings, painted another post-war shade Paint, Exterior Steel helmet, Flat Green No 3-213 and stock-piled. A vendor in Kingston Ontario had a stack of them a few years ago. (note, the photos have slipped to the bottom of this post)
And finally, a number of US M1917s reached Canada, probably the result of an August 1940 arrangement whereby the USA agreed to sell surplus equipment to Canada, for use in continental defence. Here is one, stamped ZAO that has been converted to a Mk.I* or shall we say M1917* The liner is dated 1942.
I think the British army was a bit paranoid about magnetic items close to their compasses, even the Mk2A chin strap was marked with an M or asterisk so it never got onto an Mk2 No.1 helmet,only Mk2 No.2's.
Of 3 Mk1*'s, 2 have magnetic rims, while the other has an stainless steel non magnetic rim.
& only one of the two magnetic rimed helmet has an M.