Ok in my searching I found this which is the first solid mention of the company serving with the 3rd Div. Now the question is did they wear the 3rd div patch at this time as they exchanged with the Regina rifles..hmmmmm
"Regiment converted from infantry to machine-gun unit December 1936 and mobilized as such on 1 September 1939. Assigned to 3rd Brigade of 1st Infantry Division. (1st Canadian Division mobilized on the pre-1938 British organization, which assigned a machine gun battalion to each brigade.) The Regiment went to the UK with the Division in December 1939. On arrival, the Division re-organized on current British lines and the three brigade machine gun regiments became Divisional troops. When VII Corps was formed in July 1940 as an anti-invasion force the Regiment was assigned as Corps troops and stayed in this role when the Corps was converted in October 1940 to The Canadian, later 1st Canadian, Corps. In January 1943 the Regiment was ordered to re-organize and became 32nd Canadian Reconnaissance Regiment, Canadian Armoured Corps, under command 1st Canadian Army. This unit was disbanded in March 1944 in response to a shortage of manpower and the lack of a need for an Army-level recce unit. Interests acting on behalf of the Regiment caused its revival and at the beginning of April it was reformed as First Canadian Army Headquarters Defence Company. The Regiment landed in Normandy on 28 July 1944. In September the Company exchanged with a Company of the Regina Rifles (7 Brigade, 3 Div.) to gain battle experience, first seeing action at Cap Gris Nez on 17 September and subsequently in the capture of Calais. On 6 October 1944 the Company took part in an attack across the Leopold Canal. They reverted to Army HQ Defence duties around 11 October. The Company was raised, at least notionally, to Battalion status in May 1945 and returned to Canada where it was disbanded in September 1945. (A 2nd Battalion served in the Reserve Army.) (To be completed)"