1. Prepare grill, or heat oven to 450°.
2. Tear 4 large (about 16- x 14-inch) sheets of aluminum foil. Put each fillet on one half of each sheet. Brush 1 tablespoon of the olive oil and the lemon juice evenly over fillets; sprinkle with salt and pepper. Fold half the foil over each fish fillet to make 4 rectangular packets. Fold the remaining 3 edges over several times to seal.
3. For relish, mix together remaining 1 tablespoon olive oil, tomato, olives, basil, and capers; set aside.
4. Place packets on grill over medium-hot coals or on a baking sheet in the oven. Grill, covered, or bake 6-10 minutes (depending on thickness of fish) or until fish is opaque in center. Carefully open packets; transfer to plates, and top with relish.