The 248th was raised in Northern Ontario and was absorbed into the 7th and 8th reserve battalions on 9 Jun 1917 https://en.wikipedia.org/wiki/248th_Battalion,_CEF
). Neither 7th or 8th Reserve Battalions regularly reinforced the 31st Bn CEF (an Alberta unit) but that is not uncommon. http://www.collectionscanada.gc.ca/obj/005/f2/005-1142.29.028-e.pdf
) The 31st Bn CEF was part of the 6th Brigade, 2nd Division http://cefresearch.ca/wiki/index.php/31st_Battalion
Looking at the 31st's history I would guess late Passchendaele or latter (ie 1918) if its the 31st Battalion
The CEF didn't use the tern Regiment, but the Home Militia did. In Canadian military speak they are almost interchangeable but do have different meanings. In May 1920 the 31st Grey Regiment was renamed the "The Grey Regiment", so that maybe his recruiting unit or post war regiment.
Getting his records will help a lot and there is lots of post on that subject