The story of Gareth's arrival and establishment in Arthur's court gets a whole book in Le Morte D'Arthur. Gareth, who is Gawain's brother and Arthur's nephew, initially chooses to keep his identity a secret, arriving incognito and asking Arthur to grant him lodging and food for a whole year, then two further requests that he won't specify. What's with the coy routine, Gareth?
When a knight travels incognito, sometimes it's because he wants to be distinguished by his deeds rather than a well-known name or family connection, which makes sense in this case. Gareth may not want to receive any favors just because he's the brother of Gawain, Aggravayne, and Gaheris, so he doesn't associate himself with them at first.
But Gareth's distancing of himself from his family continues even after his identity is widely known. Disavowing any role in Sir Lamerok's death, Gareth says to Trystram about his brothers, "I meddyll nat of their maters; and therefore there is none that lovyth me of them. And for cause that I undirstonde they be murtherars of good knyghtes, I lefte there company" (416.4-6). It seems like our Gareth is not a big fan of his brothers, who are neck-deep in family drama. He'd rather stay above the fray.
In fact, the relationship that defines Gareth more than his family ties is his devotion to Sir Launcelot. As a young man, Gareth demands to be knighted by this man he loves best in all the world. Of course it's about more than just affection for Launcelot. By associating with Launcelot, Gareth aligns himself with the world of chivalric courtesy and honor represented by him, rather than with the tribal blood feuding of his brothers, and that seems like a good alternative, right?
What Gareth's presence in the story tells us is that a separation from this world of blood feuding is possible even for those who are born to it. Stopping the cycle of violence is totally doable. So by comparison to Gareth, Gawain, Aggravayne, Gaheris, and Mordred seem all the more blameworthy for the pain they cause. Gareth's honor makes these dudes look downright petty.