Rub the tenderloins with lime juice and set aside 15 minutes. Add the Jerk Marinade and turn to coat meat well. Cover with plastic wrap and refrigerate for at least 4 hours or up to overnight.
Preheat a grill to medium-low. Remove the meat from the marinade, leaving some of the marinade clinging to the surface of the meat. Season the meat with the kosher salt and lightly oil the grill grates. Place the tenderloins on the grill and cook, turning occasionally, until the pork is just cooked through and nicely browned on the outside and a thermometer inserted into the center registers 145 to 150 degrees F, 28 to 30 minutes. Remove the tenderloins from the grill and allow to rest for at least 10 minutes before serving. When ready to serve, slice the tenderloins into 1/2-inch thick slices on a slight diagonal and serve fanned out on a plate,.