Place lime juice, olive oil, garlic, salt, and oregano in a large resealable plastic bag. Shake sealed bag until ingredients are well mixed. Taste the marinade for tartness. If too tart, add a little more oil. Not enough zing, add more lime. The garlic and salt flavors should also be up front, yet not overpowering. Place tenderloins in the bag, seal, and turn to coat. Marinate in the refrigerator for 2 to 5 hours.
Preheat grill for medium heat.
Lightly oil the grill grate, and discard marinade. Grill tenderloins for 20 to 30 minutes, turning once, or to desired doneness.