I see that you are again getting no responses
My local, Sigma Iota Phi, no longer exists (having become a chapter of AEPhi) but here's what we had.
Our badge was the Greek letters in silver, set in sequence, with an amethyst in the circle of the phi. At one point we got "Alpha chapter" guards. Unfortunately I don't have a picture.
We had pledge rings instead of pins. This was a deliberate decision on the part of the founders - to do something different from what other GLOs did. The pledge rings were plain silver with 1 malachite and 2 amethyst beads. The amethyst was our official jewel, and our colors were green and purple, hence the malachite. During your pledge period you were required to wear the ring at all times. After initiation you could wear it whenever you chose except during a subsequent class's pledge period.