Mine started with the 'grease' marks, where it looked shiny in some spots (generally underneath the band where it lays on itself) but then started peeling (as mentioned and shown in other threads). I contacted Apple, and they put me in touch with an 'iOS Senior Advisor' who was very patient with this situation. He mentioned that he had ordered an Apple Watch and couldn't wait until it arrived. I told him what was happening and he immediately offered to send out a new BSB to me at no charge, and never mentioned anything about sending in the defective one.
The strap got here a couple of days ago, but I wanted to keep using this 'defective' band until it got worse. Since then it started peeling in 4-5 different areas all over the top and bottom of the band, and I finally switched it out because it was getting pretty noticeable. Here's hoping that this one is fine #