Butterfly the pork tenderloin: Keeping your knife parallel to the cutting board, make a cut down the middle of one side of the tenderloin, going only halfway through the circumference. (Do not cut all the way through.) Open the tenderloin like a book so that the cut side faces up.
Blend the olives, olive oil, lemon juice, and Italian seasoning together until it forms a paste. Spread along the inside of the pork.
Starting with one of the long sides, roll the tenderloin up into a log, like a pinwheel. Using kitchen twine, tie the tenderloin together and knot at both ends. Season all sides of the tenderloin with the salt and pepper.
Preheat the oven to 375°F. Melt the butter in a large oven-safe frying pan over high heat. Sear tenderloin for 2 minutes on one side, turn to sear for 2 minutes on two more sides. Turn the tenderloin one more time, then transfer the pan to the oven. Bake for 15 minutes, or until the juices run clear.