What I did was I took my seam ripper and removed the stitches that held the binding on in the area that I was going to remove. I did not cut the binding or rip out stitches any farther than was necessary.
I have the binding all sewed back on. There was a rubber substance on the bottom of the mat, so to sew this, I placed a piece of tissue paper under the bottom of the mat. If I did not use this, it would drag on the sewing machine and be unable to advance to sew. This is what the rubber substance is for, to hold the mat in place and it did a really good job of that. The tissue paper enabled me to sew easily. After sewing, I just tore away the tissue paper off of the back side of the mat.