My understanding is that the company was "loaned" i.e. came under operational control of the Regina Rifles for the brief periods of time mentioned. I shouldn't speak too soon as I've never seen photos of the company during the period in question, but I've not seen reference to any change in formation insignia. In action, the tendency was to remove distinguishing marks as a matter of security rather than spend a bunch of time adding new badges. For the very brief period of time the RMR were in action, a change of formation patch would have been unusual - but then again, possible, also for security purposes. I've just not seen any reference to it. My understanding was that the RMR still belonged to 1st Canadian Army, but was loaned to 3rd Division to acquire battle experience. (An interesting comparison could be made to the bodyguard details of SS Leibstandarte Adolf Hitler and the Führer Begleit Bataillon of the Division Großdeutschland of the German Army, which also rotated defence details between FHQ (Führer-Hauptquartier) and the front lines.)
I've mentioned the actions of the RMR at Calais on my webpage at
which may be of interest to you. There was nothing in the source about a change in insignia.
During strategic moves of I Canadian Corps in Italy, vehicle markings were sometimes altered, and unit battledress ordered changed to fool enemy intelligence gathering efforts. Don't know how widely this was practiced in NW Europe; by 1944 the main concern was keeping a discrete appearance so as not to draw the attention of German snipers.
As DT suggests, consulting the regimental museum would be a good way to get a detailed answer to this question; may also wish to consult the archives in Ottawa in person and dig through files to see if any references are made to questions of insignia.