Preheat the grill to medium-high heat (about 400°F / 200°C).
Season the turkey loins evenly with salt, pepper, garlic powder, and smoked paprika. Drizzle lightly with olive oil.
Sear the loins directly on the grill grates for about 3–4 minutes per side, just until browned with grill marks.
Transfer to a cast iron skillet or other heavy oven-safe pan placed on the cooler side of the grill (or directly over medium-low heat if using a gas grill). Close the lid.
Finish cooking in the skillet for 15–20 minutes, turning occasionally, until the internal temperature reaches 165°F (74°C).
Rest the loins for 10–15 minutes on a cutting board before slicing thinly against the grain.