The best way to remove iron-on patches is to use a heavy-duty adhesive remover product such as Goo Gone, or the original version of Goof Off. Both solvent products are designed to remove decals, stickers, adhesives and glues.
Thoroughly soak the back area of the patch with either Goo Gone or Goof Off. Let the solvent sit for three to four minutes. Wipe the solvent residue off by dabbing the front patch area with a paper towel. Apply the solvent to the front of the badge, blotting away any residue from the back area with a paper towel. Repeat the process until all adhesive is removed.