This is probably a tip that has been covered before and I am sure that there is a special tool for this but....
I am in the process of removing the rear axle to clean it up, redo bearings, brake lines etc... Anyway I have been stumped with how to remove the parking brake cable from the backing plate. A few days ago the thought came to me to use a hose clamp on the brake cable to squish the "clip" (I don't know what you call that thing) so that I could push it through the backing plate. It worked perfectly
So to remove the parking brake cable from the backing plate use a small hose clamp. See the pictures below.
'67 Coupe 289, 2V, C4, Bench Seat.