Do you mean this on Emma’s community?
That’s a different issue (in my mind) related to how Emma search works, and can be solved entirely by Emma.
Even though editing notes in Monzo affects the reference as displayed in Monzo, I don’t think it affects what gets read by third party providers by the API. The underlyring “description field” (which Emma uses to extract payment reference details) does not seem to get edited when notes field is edited in Monzo.