Combine a few squirts of liquid dish soap with warm water in a bucket and clean the leather sofa with a sponge using the soap and water mixture.
Dry the leather sofa with a hair dryer until all the moisture is gone from the surface and the leather is visibly dry.
Sand over the peeling leather gently with 240-grit sandpaper until the peeling pieces are gone. Do not sand too much or you may cut into the leather itself. You are only trying to "clean" off the surface.
Spread leather repair compound over the sofa with the applicator included with the compound. Set the hair dryer on its lowest setting and hold it about 9 inches away from the leather sofa. Dry the leather repair compound with the hair dryer.
Apply a coat of leather color coating with the compound applicator or use a brush, following the manufacturer's coloring balance instructions so it matches your leather sofa. Let the coating dry as directed by the manufacturer.
Sand over the repaired area very lightly with 400-grit sandpaper. Then wipe down with a cloth and apply a coat of leather conditioner with another clean cloth to finish.