Mine started peeling as well. I scraped off the part with my fingernail and I figure when it gets worse I'll just stick a piece of duct tape over it. No one will see it anyhow.
Mine went bad about 8 months ago; I too smoothed them down and then placed clear shipping tape along the back side of the pull.The tape can't be seen and it has been working fine. I like OC Xfire's solution with the Corvette leather covers and ordered two in gray just today.