On November 25, 2009 Ancestry.ca completed the online launch of the Canadian Passenger Lists, 1919-1924. I visited Ancestry.com and did a search in this new database for people born in Greece -- 1,065 results were returned. As usual, there are some results that don’t seem to make sense, but most are Greek surnames. If you have ancestors that arrived in Canada during the 1919-1924 time frame, this may be a very helpful resource.
Apparently this is the only online source for this data to-date. Remember that if you don’t want to purchase a membership to Ancestry.com, most libraries have an Ancestry.com version that you can use in the Library for FREE. - Also, Ancestry.ca is currently offering a 14 day free trial.