If there's a smell emanating from the ice cubes you are using to cool your drink, you'll need to go to the source to get rid of it. Ice cube trays are made from plastic, a porous material that easily absorbs odors and holds onto them. Cleaning your ice cube trays is a chore most people never think about. After all, the only thing that goes in them is water. When ice cube trays need a good cleaning, they let you know in the form of a noticeably unpleasant smell.
Wash the ice cube trays with warm soapy water and a clean cloth or sponge to remove any surface bacteria that may be contributing to the odor.
Add a cup of white vinegar to a gallon of water and submerge the trays in it. Leave them to soak for at least two hours before rinsing them off and allowing them to air dry.
Clean out the freezer if you suspect it's been a while since you've done so. Odors from the freezer can cause your ice cube trays to smell, and ultimately the ice cubes you put in your drinks will smell too. Remove all the food, turn off the freezer and allow it to thaw before washing the inside with warm soapy water. Wipe the inside carefully with a clean, dry towel and turn the freezer back on.
Place a box of baking soda in the freezer to help cut back on odors that might eventually end up in your ice tray. Make sure that all foods are packaged well and wrapped in plastic to prevent further odors.