Mix several drops of tea tree oil with 1-2 capfuls of peroxide. Rinse your cup well with hot water, then dip an old toothbrush in the solution and scrub the cup inside and out. Then rinse the cup and the brush and sprinkle a little baking soda into the cup. Use the brush to distribute/scrub the soda all over the cup so it breaks down the oily solution, then rinse well in hot water.
*If you have the time, try diluting the TTO/peroxide with just enough water to submerge the cup and let it soak overnight. Then follow it with an overnight soak in baking soda solution.
*If the TTO smell (it's minty!) lingers on your cup and you're not too keen on shoving it up your box that way, try wiping with alcohol or washing in soap and water. (I didn't bother with either, so mine still smelled TTO-y when I put it back in. It didn't irritate my bits, just made them feel a little tingly and cool. TTO is recommended as a treatment for yeast infections, so it's likely to be friendly to your vag.)