Main question is: are you allowed to use Canadian Coat of Arms in the web design? See details for the answer.
The answer is yes, if you get he supporting documents from the Treasury Board of Canada Secretariat (TBS) that you are allowed to use it, or if the company who ordered website design is related to Canadian government and have permission to do so. Canadian Coat of Arms falls under the laws for Corporate Identity and copyright laws.
Full information provided here: http://www.tbs-sct.gc.ca/fip-pcim/man-eng.asp