Wash the fennel bulbs and the tomatoes and cut them into thin slices. Set the fennel greens aside. Cut the garlic clove into thin slices as well. In a bowl, mix olive oil with some lemon juice, garlic and salt. Add the vegetables to the marinade.
Tear off 4 sheets of aluminum foil. Divide the fennel and tomato mixture among the foil pieces and place a sprig of thyme on each.
Fold the foil and place the vegetable packets on the grill. Cook the vegetables until soft.
Remove from foil and arrange on plates.