Take one spudger and fit it under the grille.

Use your first spudger to pry up and make room to insert a second one.

Sever the glue connections between the grille and the device by moving one spudger around, cutting through the glue.

Use the other spudger to raise the grille, allowing you to see where you're working.

Since you're cutting the glue, the grille may not stick as well when reassembled.