Is this machine EMB? Do you have a picture to post?
Are the wrinkles around the design? Did you hoop the towels and what stabilizer was used for the project? Design stitch count? Dense designs can have pull that distorts the finished design.
It can also be from the weave of the towels.
The wrinkles can be caused from the stabilizing technique used. I generally hoop if the project can be hooped and use a basting block.
For the next time, try a design that has an open stitch to it over ones that have dense fill stitches.