The suction cup of my Pro Tech Toolkit neither worked on tape nor screen, so I took the blade of my titanium scissors, pressed it against the side of the screen and lifted it while trying to find my third hand to put a spudger into the opening gap. This worked well in the end, but be careful.

This step should also include hints about putting the new screen into its place. I was happy to press mine gently into the frame from edge to edge, feeling it bend but not break.