The tray under your mesh floor is best if it is sealed in a way that prevents bees,wasps,beetles and other insects from entering.
Anything that gets in looks for a tasty snack and varroa fits that bill
Most of the designs sold have a lightweight correx sheet under the mesh which is open to the elements That's maybe ok in winter but pretty useless in the warmer months.
The best check is to stick some thymol treatment over the bees and see what drops out