When I joined my local, bigs and littles exchanged gifts. We had a paddle party at the local greek store; I gave my big a paddle, and she gave me a wooden cutout thing with our names and letters (which I haven't seen since the last time I moved
).
Once we went AEPhi, the idea of littles giving their bigs a gift died out. Occasionally a little would choose to give her big a gift. My big (from the local) was one of the women who spearheaded the effort to join AEPhi. So I made two identical cross stitches of the AEPhi letters and a sprig of lily of the valley. I have one, and I gave the other to my big at the time of our initiation. But that was of my own free choice, and when we went AEPhi, we were all the Alpha new member class, on equal footing.