This patch is not an obvious patch. It was done using a very sophisticated technique developed in France in the 16th Century to repair wall hangings, tapestries and arras, called French Invisible Reweaving. It involved making a yarn as close as possible to the original in color, size, etc., and then carefully splicing the new yarn to the old and then reweaving to match the extant weave. On the Shroud, the area under discussion is on the lower left corner, a corner that was often used to hold or mount the Shroud when it was displayed horizontally and would be a corner that experienced wear and stress tearing. What is now known, that was unknown to the scientists who cut the sample from the Shroud in 1988, is that the repair yarn is COTTON... while the original Shroud material is LINEN, derived from Flax. The new yarn has also been dyed to match and contains Aluminum (in the form of Alum) which was added as a mordant in the preparation of the yarn while the main body of the cloth contains no Aluminum at all. What the scientists cut as a sample to be Carbon tested in 1988 is a mixture of original Linen and more modern Cotton.
The other tidbit I picked up from the program is that the sample was selected not by the scientists or the photographers who knew that corner was contaminated.