As far as I recall, there were a limited number of times the organization was mentioned:
Tristran shows that he is beginning to care more for the star. They are rescued by a passing sky-ship, on which Tristran's hand is treated and bandaged. The captain of the ship reveals that he is a member of an organization which is later referred to as the "Fellowship of the Castle", whose agents have been working to ensure Tristran's safe return to Wall. The man who gave Tristran the candle was also a member of this fellowship. The ship sets them down on the road to Wall
And the latter mention:
After Tristan's death, there were those who claimed that he was a members of the Fellowship of the Castle, and was instrumental in breaking the power of the Unseelie Court. But the truth of that, as so much else, died with him and has never been established either one way nor another.
The Fellowship of the Castle was also mentioned in The Tale of Sir Lancelot, which might offer a clue behind the meaning in the Neil Gaiman novel. However, it too was seemingly only mentioned in passing, making it difficult to determine its meaning. Sources are also in old English and are difficult to interpret.
Sir Launcelot waxed so faint of fighting and travailing, and was so
weary of his great deeds, that he might not lift up his arms for to
give one stroke, so that he weened never to have borne arms; and then
they all took and led him away into a forest, and there made him to
alight and to rest , him. And then all the fellowship of the castle
were overcome for the default of him. Then, they said all unto Sir
Launcelot: Blessed be God that ye be now of our fellowship, for we
shall hold you in our prison; and so they left him with few words. And
then Sir Launcelot made great sorrow, For never or now was I never at
tournament nor jousts but I had the best, and now I am shamed; and
then he said: Now I am sure that I am more sinfuller than ever I was.
Kellscraft: King Arthur
and
At last it seemed to him that the black Knights nearest the castle
fared the worst, so, as he ever took the part of the weaker, he rode
to their help and smote many of the white Knights to the earth and did
marvellous deeds of arms. But always the white Knights held round Sir
Lancelot to tire him out. And as no man may endure for ever, in the
end Sir Lancelot waxed so faint of fighting that his arms would not
lift themselves to deal a stroke; then they took him, and led him away
into the forest and made him alight from his horse and rest, and when
he was taken the fellowship of the castle were overcome for want of
him. 'Never ere now was I at tournament or jousts but I had the best,'
moaned Sir Lancelot to himself, as soon as the Knights had left him
and he was alone. 'But now am I shamed, and I am persuaded that I am
more sinful than ever I was.' Sorrowfully he rode on till he passed a
chapel, where stood a nun, who called to him and asked him his name
and what he was seeking.
Tales of the Round Table: AN ADVENTURE OF SIR LANCELOT (1902)