Make the tomato salad: In a large bowl, mix together all the ingredients and set aside.
Make the gremolata: Place all the ingredients in a bowl and mix. Set aside.
Make the halibut: Place the olive oil and lemon juice in a large baking dish (or you can use a re-sealable baggie). Rinse the fish and pat it dry, season with the salt and pepper. Place the fish in the dish or re-sealable baggie, turning once to coat with the marinade. Let the fish marinate for 10 minutes at room temperature.
Scatter the clean arugula on a 19-inch round or oval platter. Grill the fish over a medium hot fire for 5 to 6 minutes per side, until the flesh is opaque through to the center. When finished grilling, remove the hot fish immediately to the platter of arugula. Top with the tomato mixture, and sprinkle the gremolata over the top of the tomatoes. Serve immediately.