1. Preheat grill to 350° to 400° (medium-high) heat. Remove silver skin from tenderloin, leaving a thin layer of fat. Rub 1 Tbsp. olive oil, 1/2 tsp. salt, and 1 Tbsp. Caribbean seasoning over tenderloin.
2. Grill tenderloin, covered with grill lid, 10 to 12 minutes on each side or until a meat thermometer inserted into thickest portion registers 155°. Remove from grill, and let stand 5 minutes before slicing.
3. Meanwhile, bring butter peas and water to cover to a boil in a 3-qt. saucepan over high heat; reduce heat to medium, and simmer 25 minutes; drain. Combine peas, next 6 ingredients, and remaining 2 Tbsp. olive oil and 1 tsp. salt. Serve with sliced pork.