There are a lot of alums in the area where my chapter is, but no formally-organized alumnae association that I am aware of. So, typically, no initiation gifts from alums.
In my case, I was a founder, and when we were initiated, the TEC who had been placed with us during our first weeks as a colony gave us acrylic badge boxes with the crest imprinted on the lid. Mine has disappeared - fortunately my badge was not in it!