If it were me I would either buy:
1) a washable piece of fabric that is either a solid color or a neutral color, measure amount of fabric to cover the back stitching, then hand or machine sew it to the guest towel.
2) buy another of the same kind of guest towel you have, cut this towel for the amount of fabric you need to cover the back of the stitched area OR stitch the same design on panel on the 2nd towel and cut out this stitched area to sew over back of first hand towel. You would then have same design on both sides.
I like the idea of the 1 example; if I found a guest towel and stitched a small winter season on the front of
It, a small red cardinal foe example, I would cover the stitching on the back with a solid red or was able to find material that has holly berry print as fabric to cover the back