Heat one side of your grill with medium-high heat. Leave the other side unheated.
Stir the oil, smoked paprika, salt, black pepper, garlic powder and onion powder in a small bowl until it makes a paste. Set aside.
Pat the tenderloin dry with paper towels. Use a small knife to remove the silverskin, the silvery-blue strip that's usually running under a thin layer of fat.To do this, use a small knife to make a small incision down into the meat at one end of the silverskin. Then with one hand, grab the little flap of silverskin you just loosened and pull it up away from the pork while you slice along the pork just beneath it. Coat the pork all over with the the paste.
Grill the pork on one side over the medium-high heat for 4-5 minutes, covered, until dark char marks appear. Then flip the pork and grill for another 4-5 minutes, covered.
Move the pork over to the unheated side of the grill and insert the probe thermometer in the thickest part of the tenderloin. Cover and let cook until it reaches 145°. Depending on the size of the tenderloin, this can take up to 10 minutes. But if it's very thin, it might not need any extra cooking time at all.
Remove to a plate, baking sheet or baking dish and cover loosely with aluminum foil. Let rest for 10 minutes.
Slice and serve, pouring over any juices that accumulated while the pork was resting.