I had thought perhaps I should provide some info on the mushroom parts... gills and veils. The veil is a covering over the gills that can peel off and become a ring (or collar) around the stem.
"Gills, known as "lamellae", are plate like structures arranged on the underside of a mushroom's cap. The common button mushroom sold in grocery stores is a gilled mushroom."from Mushroom Expert.com
You can see gills, a veil, and the resulting collars or rings in the pictures on both "real" mushrooms and some of my latest "made" ones.