The covering on the stitching of your embroidered product is called an embroidery backing.
The backing is placed under the design to help stabilize the stitching. It helps to protect the garment and prevents wrinkling and puckering during the stitching process.
Please don't tear off the backing. After the first few times the product is washed, the backing will either dissolve or become smaller and less noticeable. If you wish, you can gently trim off excess backing with scissors.