I can't actually say a lot about this other than the fact that it seems inspired by the symbols of Freemasonry, which is not surprising if it's true that the Knights of Eastern Calculus, like Freemasons, are at least partially derived from the Knights Templar. I will gladly defer to anyone with more experience with this type of symbolism. Until then, here's my take:
The most obvious Masonic symbol present in the Knights symbol is the compass in the center. However, the Knights' compass differs from the standard compass of Freemasonry in that the points of the compass converge instead of diverge. In Freemasonry, the compass is almost always shown with the Square. There is no clearly discernible Square on the symbol of the Knights unless you count the bottom patch of orange, which is roughly in the right location and roughly the right shape if you stretch your imagination. More convincingly than shape and color, perhaps, is the fact that both the bottom half of the Knights symbol and the Masonic square have increments marked on them.
The "mountain" in the center is reminiscent of the pyramid on the US dollar bill, which is full of Masonic symbols itself. In that sense, the "mountain" may be said to represent the unfinished Temple of Solomon, which was supposedly the home base of the Knights Templar (and where they hid their "secret treasure"). There are 14 light-colored stones on the top, but I am unaware of their significance. Furthermore, not counting the red symbol (the Blood of Christ?) at the very top, there are 14 men-shaped (?) figures along the upper outer rim of the Knights Symbol. If there are any savvy numerologists out there with insight on the number 14 in the context of serial experiments lain, please let me know.
[Update (3/31/2000): thought experiments lain reader J. Michael Rollins suggests that the 14 figures might represent each member of the Majestic 12 plus John Lilly and Ted Nelson, as those are the 14 people mentioned and pictured in layer:09 "PROTOCOL." Furthermore, the red symbol at the top might represent Eiri Masami, the "God" of the Knights.]
The crescent on the top of the compass may represent the Moon, which of course has all kinds of mystical significance, making it difficult to figure out exactly what it means here. Likewise, there is a sun in the center of the symbol. Alternatively, that might be the "Eye of God" such as the famous Eye in the Pyramid on the dollar bill. Regarding the crescent and the red cross-like symbol at the top, perhaps the red cross represents the crucifixion and the crescent represents the Holy Grail into which the blood of Christ falls.
I wasn't expecting to find anything, but when I compared the Copland OS symbol with the Knights symbol, I saw some resemblance. If there really is a resemblance, I have no idea what it's supposed to mean, except that maybe the Knights are or were (through Eiri Masami, probably) somehow associated with Tachibana Lab. Perhaps there are secret Knights (Eiri and/or others) who have infiltrated Tachibana Lab. Or for an even wilder theory, perhaps the Knights themselves are controlled by Tachibana?! I think it's the former and not the latter, but you never know...
To convince myself that the Copland OS symbol truly resembles the Knights symbol, I resized the COS symbol so that the outer circle is roughly the same size as the outer circle of the Knights symbol. I then cut-and-pasted parts of the COS symbol onto the Knights symbol to see how well the parts correspond. The results of this "experiment" are below: