Rubberbanditz bands are made through a layering process (thin strand of latex spooled) instead of one solid molded latex. The result is higher quality with the layering process - longer durability, smoother increase in resistance as the band is stretched (i.e. better user experience).
With friction, resistance bands can peel over time due to normal wear and tear from use. You can snip off the piece that is peeling then the band should maintain its structural integrity, prevent any further peeling, and continue to use as is.
We'd also recommend rotating the band around the pull-up bar so it doesn't wear one place. Also, make sure it's not wrapped around a rough portion of the pull-up bar. Of course, if the edge of the band has a cut in it, then it should not be used as it may snap on you.