The fabric tape around the edges of the wafer is pretty much superfluous. It adds a little bit of stability to the "important" part of the wafer but many people get by completely without it. For example, look at this setup (scroll down to the first big photo): http://ostomyoutdoors.com/2012/06/12/skin-sleuthing/ She's cut the tape off *completely* and just uses a few strips of a less irritating kind of tape.
As long as you aren't having leaks or skin irritation, don't sweat it.
dx'ed UC pancolitis 5/12
past meds: asacol hd, VSL#3, apriso, rowasa, xifaxan, 6mp, cortifoam, pentasa, cimzia, canasa, butyrate, flagyl, cipro, prednisone, remicade, methotrexate, cholestyramine, cortenema
current meds: none!
step one: colectomy, end ileo 1/16/13
step two: j-pouch construction, loop ileo 5/1/13
step three: takedown 7/31/13