Machine wash and dry your towel. This prevents warped seams in the future by preshrinking the fabric.
Cut a 9 3/4-by-7 1/2-inch piece of towel.
Fold the 7 1/2-inch ends of the towel to one side 1/4 inch. Iron the folds. Fold the ends another 1/4 inch, and iron them again. Sew along both folded ends with an 1/8-inch seam allowance.
Lay the towel on your work surface with the right side facing up -- the side you didn't fold the ends to -- horizontally oriented. Fold the left and right sides of the towel in to the middle 3 1/4 inches. They will completely overlap each other in the center. Sew along the top and bottom edges with a 1/4-inch seam allowance.
Turn the fabric pouch right side out through the opening where the left and right sides overlapped.
Fill a snack-size plastic zipper bag two-thirds full with dish soap. Close the bag. Tuck that bag in a second zipper bag with the zipper of the first bag at the bottom of the second. Zip the second back.
Stick the double-bagged dish soap in the freezer overnight. Take it out in the morning and tuck it in the fabric pouch you made before placing it in your lunch bag.