These adhesive-bound appliqués come in a variety of colors, shapes, and sizes, and are designed for bathtubs that aren't manufactured with an integral nonskid surface. They serve a very important purpose especially since studies have shown that the majority of home accidents occur in or around bathtubs. However, they do tend to deteriorate over time and need to be removed and replaced.
If your tub has a porcelain finish, the most effective method of removal is a sharp razor blade. Any adhesive residue that remains can be removed with a mild detergent and warm water. Fiberglass or acrylic tubs pose a more difficult problem. Their finish can be easily damaged if great care is not employed. Do not use a razor blades here. Manufacturers of these synthetic products recommend using acetone and a clean, soft cloth. Remember safety first. Make sure that there is adequate ventilation when working around acetone vapors.
Should you not be successful in removing the appliqués, there are firms that specialize in tub refinishing. Some are even equipped to install a new clear, non-skid surface over the entire area.