Join Date: Aug 2005
Location: Pittsburgh, PA
Bikes: '''96 Litespeed Catalyst, '05 Litespeed Firenze, '06 Litespeed Tuscany, '12 Surly Pacer, All are 3x8,9 or 10. It is hilly around here!
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First. I'll assume you've removed the lever fixing bolts and the levers themselves.
The backing plates (that's what those curved inner pieces are called) have square holes that are just a friction fit on the braze-on lugs so they should remove fairly easily. Have you tried just to pull them straight off by hand? They usually come off that way without too much effort.
Otherwise you can pry them off with a small screwdriver or knife blade between the frame and their inside edges. Be careful not to gouge them or scratch the frame.