Heat grill. Brush turkey tenderloins with oil; sprinkle with salt and pepper. In small saucepan, combine salad dressing and basil; mix well.
When ready to grill, place turkey on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals; cover grill. Cook 15 to 20 minutes or until turkey is fork-tender and juices run clear, turning and brushing with salad dressing mixture 2 or 3 times.
To serve, bring any remaining salad dressing mixture to a boil. Serve with turkey.