Some pictures of Training squads have passed through ebay recently.
I searched Guards Machine Gun then clicked on completed items.
https://www.ebay.co.uk/sch/i.html?_f...&LH_Complete=1
There are a number of forum threads if you search Guards Machine Gun. I would think your relative would have worn the GMGB badge, and 'possibly' the later badge, but not sure of the earliest I have seen it worn in 1919- it is very scarce in pictures. The ones in pictures I link to are mid 1919. Regards, Paul. (a good GMGR badge is very scarce)
Further- this thread has good info.
https://www.britishbadgeforum.com/fo...chine+regiment
The name changed in May 1918, but it could well be the new badge was not worn until April 1919.