Muzzle brakes are indeed covered by itar. You would be breaking U.S. law by taking it out of the country with you.
If not ITAR restricted why not save yourself the possible hassle of having to explain it at security by simply mailing it to yourself ?
I read in a separate posting here that brakes aren't covered. Only flash hiders. That is why you can order them from the states. Only problem is the Brownell does not ship items above $100 to Canada.
How does a muzzle break violate law if it's in flown baggage as opposed to driving across or having it mailed?
Because its a gun part being exported by someone who is not a licenced exporter?
Mailed across the border = export.
Hand carried across the border = export.
Driven across the border = export.
Chucked over the border with a slingshot = export.
Attached to a carrier pigeon and flown across the border = export.
Get the idea?