If you forget to say Al Hanisim in bentching on Chanuka or Purim, you can add the הרחמן later to make up for it (Rama 682:1). You can also do the same thing in Shemoneh Esrei, provided that you similarly phrase it as a request (Mishna Berura 4).
Why is the makeup phrased as a request instead of thanks? At least for Chanuka, the holiday is defined as days of הלל והודאה (Shabbos 21b), and Rashi connects הודאה directly to Al Hanisim. Making up for it as a request seems to defeat the entire purpose.
Why can't you make it up phrased as thanks? (Is it because of מודים מודים? That's all I could think of, but I'd like to see someone say it explicitly.) And, given that you can't for whatever reason, why make it up at all?