According to EG, a resident of New Orleans, Muses is one of the first all female parades in Mardi Gras. To set it apart from the other parades they started throwing decorated heels. Each rider decorates their own shoes and put their spin on them, with glitter, writing, and designs. It turns into a pretty sculpture of a shoe. Each rider decorates 10-12 shoes and throws them off of their float during the parade. She has caught 3 shoes in her time at Mardi Gras and she considers it a symbol of New Orleans Mardi Gras. Because of muses other parades have started to throw other items like it. Other parades like the Krewe of Tucks and the Krewe of Nyx throw decorated toilet plungers and purses respectively.
EG is a college aged resident of New Orleans. She was born there and has lived there her entire life. This was collected in a conversation at my home. She has been to Mardi Gras every year since her birth and considers it to be a central part of her life.
I, also being a resident from New Orleans, understand this piece of folklore very well. The heels thrown from the float are a sub-genre of what is know as throws, or things float riders throw off a float during a parade. Beads and Doubloons are what people mainly consider as Mardi Gras throws, but there are many more. Cups, spears, and as EG mentioned, heels and other decorated items are all throws that separate one parade from another. I think the main reason for these throws is that each has a distinct item that not only tells a story of the rider and the parade, but something you can only get if you participate in or go to the parade during the season.