Drop it in some hydrogen peroxide or denture cleaner.
On a related note, I would go back and insist that the orthodontist cement an internal retainer to your teeth. Basically, its just a long strip of metal they cement to the back of your teeth and serves the same function as a retainer appliance. Its invisible to others, barely perceptible to the wearer, and can stay in there for like up to two years while your teeth 'settle' to their new positions.
Retainers are too easy to opt-out of wearing, lose, and break accidentally. My retainer was far more uncomfortable and annoying than the damned braces were, except I couldn't take my braces off, but I could opt-out of wearing my retainer like I was supposed to.
So that's what I did and my teeth moved back to the same position they were before my braces. About $3500 down the toilet (this was 15 years ago). Plus, this strip of metal is about 1/4 of the cost of a retainer appliance, and will not 'break' or need replacement, which is why many orthodontists don't tell you about it, they want to make more money. I didn't even know about this option until about two years after my braces were removed. My orthodontist never mentioned it.
I had to have my retainer replaced about three times, one accidentally thrown in the garbage, and the other two were broken in accidents, which are common reasons for retainer replacement. Each replacement was about $250, and the orthodontist happily replaced them because he was making more money.
That all could have been avoided if my orthodontist wasn't a greedy idiot and I told him so when I went to see my dentist one day (they shared the same building).