Comment 8 for bug 1391259

 Alt+Right Click is very nice *once you KNOW it*

A more intuituve choice would be extending the grabbable area outside the narrow border to make it easier to hit.

I don't remember which windowing system it was (gnome-x ?), but somewhere sometime there was an option to define how much the mouse cursor would "stick" to the border. I.e. when you try to move the mouse slowly out of a window, the cursor would keep jumping back to the border making it easy to grab. Jerking the mouse a bit, or moving fast allowed you to cross the "magnetic" border. Another advantage was that it stopped your mouse from accidentally wandering to an other window when having focus follow mouse.
That's what I would vote for, if it was doable in Mate.