Pull up on the suction cup with firm, constant pressure to create a slight gap between the screen and the frame.

Insert an opening pick into the gap under the screen's plastic bezel.

The watertight adhesive holding the screen in place is very strong; creating this initial gap takes a significant amount of force. If you're having a hard time opening a gap, apply more heat, and gently rock the screen up and down to weaken the adhesive until you create enough of a gap to insert your tool.