The H2O2 probably does. H2O2 can act as reductor and as oxidizer. E.g. when you add 30% H2O2 to 30% HCl, then Cl2 is formed (oxidation), but after a while, O2 is formed and Cl2 disappears (reduction). This reaction can even oscillate.
A similar thing is known for oxidation of ferrocyanide and reduction of ferricyanide with H2O2. So, it would not surprise me when it also shows similar behavior with Fe(3+) ion.