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For the Relish, heat oil in medium skillet on medium-high heat. Add onion and garlic; cook and stir on medium heat 3 minutes or until softened. Add 1/2 of the grapefruit segments and bell pepper; cook and stir 30 seconds. Remove from heat. Stir in honey, basil, salt and red pepper. Set aside.
Grill oysters, flat-side up, over medium-high heat 3 to 5 minutes or until oysters begin to open. (Discard any oysters that do not open.) Remove oysters from grill with spatula or tongs. Remove the top shells with pot holders. (Oysters will be hot.) Loosen oysters from the bottom shells with paring knife.
Top each oyster with 1 teaspoon of the Relish and 1 of the remaining grapefruit segments. Grill oysters 3 to 5 minutes or until heated through. Sprinkle with parsley. Serve immediately.