Trim the tenderloin of any excess fat and silver skin and allow to stand at room temperature for 20 to 30 minutes before grilling. Lightly brush or spray with oil and season with salt and pepper. Sear over Direct Medium heat until well marked, about 15 minutes, turning a quarter turn every 3 to 4 minutes. Continue grilling over Indirect Medium heat until cooked to desired doneness, 15 to 20 minutes longer for medium-rare, turning once. Remove from the grill and let rest for 5 to 10 minutes. Cut into 1/8-inch slices.