I whipped it up in five seconds to call your bluff, sorry. Your average pretender to relativity won't know what a Minkowski diagram is.
Taking you significantly more seriously: Yellow lines are the reference frame of the teleporter. The teleporter starts at the origin, instantaneously accelerates to the velocity indicated by the yellow lines, teleports against his direction of travel, instantaneously decelerates, and teleports back to his original position; blue lines therefore trace spacelike paths, since teleportation takes place along a line of simultaneity. When the teleporter reaches the end of the blue line, he is separated by a negative timelike interval from the beginning of the blue line; Novikov aside, he is capable of "changing the past."
Re: Time Travel?
Taking you significantly more seriously: Yellow lines are the reference frame of the teleporter. The teleporter starts at the origin, instantaneously accelerates to the velocity indicated by the yellow lines, teleports against his direction of travel, instantaneously decelerates, and teleports back to his original position; blue lines therefore trace spacelike paths, since teleportation takes place along a line of simultaneity. When the teleporter reaches the end of the blue line, he is separated by a negative timelike interval from the beginning of the blue line; Novikov aside, he is capable of "changing the past."