In my opinion the proper way to deal with excessive wear of handbrake pads is as follows.
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If there is not one there already put a small cylindrical compression spring on the adjusting screw, between the pads so that it pushes the pads apart.
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Each pad has a lifter attached to the pad holder, it’s like a washer with a long tab sticking out of the side and is bent into a Z shape. Ideally I expect these should be made of a spring metal, but they are not (well mine are not); so as the pads wear, this gets pressed further down and does not recover its original shape. When you fit new pads it is important to bend the end (that is furthest from the bolt hole) upwards gently, so that it properly lifts the handbrake pads away from the disk when the handbrake is released.