I have a 2010 Prius IV, VIN JTDKN3DU9A1011549 and at about 40,000 miles the pad on the parking brake arm fell off. I put it back on but it kept falling off. I made sure the square protrusion on the inside-right was pressed into the rectangular hole on the parking brake arm. This design is supposed to keep it in place but it didn't. So, I ordered a new one from our dealership hoping the design would be improved. When it came in I matched it up and it was the same. I didn’t see any design changes. The parts clerk told me there was a service bulletin out on this part and that it stated that if it fell off it was to be glued back on. That was an unsatisfactory solution so I asked the clerk to find another part that would work. He found another brake pad that he said should work but didn't state which year or model Prius on which it was to be used. The part number for the second pad he ordered is 46252-47010, Pad, Parking Brake. When the pad arrived I compared it to the pad that was on my car when it was manufactured. The replacement pad was designed slightly different in two ways. First, the piece that inserts into the side of the parking brake arm was rectangular in shape, providing about 1/8" overlap on the inside top of the brake arm. Second, on the back one of the corners has a triangular flap of rubber that makes it more difficult for it to fall off. (The attached document shoes both the original and the pad I used to replace it.) Although this is not the correct part for my car, per the online parts catalog, I believe it is better than the one that was on it when manufactured. It is not necessary to use glue on it to keep it in place. The reason I decided to post my experience is that I believe Toyota should have issued a service bulletin that calls for the original part to be replaced by the part 46252-47010, not to glue the same type off pad in place. The old pad could be easily replaced by the new pad during an oil change, or other scheduled service.
When I stated reading your post. I thought you were talking about the brake pads. To avoid confusion, that's usually called a parking brake pedal cover.
Doubtful that the little extra corner would make much of a difference. Keep in mind that the rubber is new and soft right now. Once it ages, hardens and shrinks, you might end up in the same boat.