Hi Ben,
Based on the description in the guide that states, "the screen is strongly adhered to the frame", I presume that to mean it's harder to remove than your average screen. They follow that up with the comment, "it requires significant heat to soften the adhesive underneath", telling me that you may need to heat the adhesive more than you might think was safe.
If you have a hair dryer, I might suggest setting it on high heat and blasting one end of the phone for something like 3 to 5 minutes before you try the suction cup; in fact, if you can position it right, leave it blowing on the phone as you try to create an opening for your pick. Again, they keep reinforcing the need for heat with the statement that you should heat it "until it's almost too hot to touch"
I generally prefer to start out with a metal pick like the iSesamo and use the plastic guitar picks to keep it from re-adhering as I go around the edge of the phone. A curved blade X-Acto knife would also be a good choice here.
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