Apple Watch Sport Band Permanently Damaged
Apple's warranty policy allows them to not cover cosmetic damage to parts however, they may not choose to deny a warranty swap if you present the band for service and are reasonable. (I don't think you'll be angry, just that I've seen people totally ruin things by rude or boorish behavior when they are angry and seek service with aggressive language or worse).

I would print out or be very familiar with Apple's cleaning guide for the product. They may decide to take back some parts for quality control that wouldn't normally be exchanged since the product is so new.


https://support.apple.com/en-us/HT204522


Do be aware that toilet paper is not lint free cloth and many brands may not even be non-abrasive. The only cleaning agent Apple recommends is water so be sure to understand if they charge for a replacement if you don't follow their recommendations. Better to take the dirty band in and ask if it's cleanable than to show up after you expanded the list of techniques.

Even if you did resort to harsh methods, asking for help is still worth its IMO.