Can't remove top piece of drain
Brute force applied carefully would be the answer in this case. It's not unusual for adhesive material to seep under the drain grille when assembled. An angled pry-bar that can fit through the mesh to get as close as possible to the edge of the circle for best leverage and minimal possibility of damage.

The square holes would give you the best flexibility of attack when approached on the diagonal.  The tricky part is to have something thin enough that won't bend when you try to pry.