That GIF simply uses a Yoyo loop, so that the tween plays forward and then backwards automatically:
myText.DOText("Final message to display", 2).SetLoops(-1, LoopType.Yoyo);
Otherwise, you could actually control it, like this:
// Set autokill to false so the tween is reusable
myTween = myText.DOText("Final message to display", 2).SetLoops(-1, LoopType.Yoyo).SetAutoKill(false);
// ... somewhere else in your code ...
// Plays the animation forward
myTween.PlayForward();
// Plays the animation backwards, cancelling the letters
myTween.PlayBackwards();