I used one of the 40% off coupons to purchase one of these cup cozies at JoAnn's Fabrics. Super cheap. That plastic button had to go to make room for one of my handmade polymer buttons.
If you would like to try your hand at making your own, Staci of Crafty Staci.com has a great free tutorial (click HERE) for a reversible cozy. Then you can add your own polymer button to complete the design.