Yes! You can eat the tops! 

Can you eat the tops! Yes! Beet greens, radish tops, turnip greens and carrot tops all are delicious!

Sautéed your beet, turnip or radish greens with onion, garlic and olive oil. Add ginger for a Asian stir fry.
Carrot tops are a wonderful addition to soup stock. Add it in and remove before adding rest of soup ingredients. 

Or add carrot tops to pesto.
There will be times when you will not get the greens either because the core group removes them so the veggies can actually fit in your box, or when the veggies arrive from the farm already removed.