The mounting screws for those pedals you've shown in pic #2 are flush head screws. They've got a "V" shaped taper at the head, and the screws would pull through the strap. You can't use a washer with those screws, and that's why they supply for mounting the PowerGrips straps.
Additionally, you're not replacing those screws with what PG supplies for you. Those flush heads attach the cage to the pedal body. The attachment hardware for the straps goes through the set of holes used for mounting clips; that's why there's a nylock nut on the backside... To keep everything tight and in place even with all the pressure being exerted on it from twisting and pedaling. If you just used the cage mount screws, chances are they'd work themselves out and you'd be left with not only a loose strap, but also a loose pedal cage.
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"I feel like my world was classier before I found cyclocross."
- Mandi M.