There definitely was an independent 3 Canadian Army Tank Brigade. And there was also a 3 Cdn Armoured Brigadge. The independent 3 CTB was the one which had the order of battle flipped and the units involved, Grey & Simcoe Foresters, Halifax Rifles, 16/22nd Sask Horse (originally 2 CTB) were transferred to 3 CTB. The original 3 CTB regiments, 1st Hussars, Fort Garry Horse, and Sherbrooke Fusilier Regt were transferred to 2 CTB. Then, in July of 1943, all tank brigades were redesignated and 2 CTB became 2 Cdn Armoured Bde. 3 CTB was not redesignated, as there was already 3 CAB in 4 Cdn Armd Div. (order of battle, Cdn Grenadier Gds, Gov Gen Foot Gds, and British Columbia Regt). 3 CTB was slated for disbandment and became a holding formation until personnel were dispersed and the formation was disbanded Nov 1, 1943.
In answer to Bruce's question, the patches that are extant were actually for the independent 3 CTB. And to confuse matters even more, the original order of battle was the basis of the numbered regimental designations imposed on the 3 CTB patches and 2 CTB patches.