After Gawain discovers that the Green Knight, whom he has spent the last year fearing, is actually Lord Bertilak, his sense of relief must be hard to compare. Instead of getting a blow from the Green Knight's axe, he receives simply a nick from Lord Bertilak, which is fairly given in retribution for Gawain not having given him the girdle that he received from Lady Bertilak.
The phrase "A man who's true to his word, / there's nothing he needs to fear" rings true in this scenario, because if Gawain had been honest and handed over the girdle, as he knew he was expected to do, he would have come to no harm whatsoever.
This idea seems to ring true to most situations in life. Life experience shows that lying and failing to honor your commitments only lead to trouble, even if it only catches up with you later in life. Being true to your word means humbling yourself at times, and as Gawain learned, there is a feeling of great redemption that comes with being true to one's word.
While there will always be things to fear in life that having nothing to do with whether or not you're a person of your word—such as becoming a victim of crime or losing someone you love—there are many fears that can be alleviated by being a person of your word, particularly in a professional or academic context.