You really need stabilizer on the back to keep the towel from stretching, thus causing puckering around the embroidery. It also keeps the fibers from sinking down into the throatplate of the machine. The stabilizer won't show after the stitching because your matching thread is covering it, and the stabilizer helps keep the stitching nice after the towel has been washed many times.

I use Vilene on top to keep the stitches from sinking into the nap of the towel. Denise

I always use water soluble on top and cutaway on back. Cutaway will let you wash the towel forever and it won't pucker when washed .