It can be cleaned! You can use a mild detergent (such as Woolite) to hand wash the grosgrain ribbon:
- Pull out the ribbon as far as it will go.
- Wash the dirty section, being careful not to wet the leather.
- Let it dry over night, or take a hair dryer to speed up the process.
That's it! Repeat the process if the first time didn't quite clean it to your liking.