This is fascinating. This keeps getting more and more interesting and challenging.
Someone posted my question on a large, helpful, internet space and got this answer:
So now a second person, when given my spoken request ("mmm-goi,") has responded with the same two characters. He says that they are used as "thank you" but translate literally to "should not." And the reason that people had a hard time reading it is that the characters are not part of standard written Chinese. (I just read a dozen Wikipedia articles on Chinese language(s) and dialects, written and spoken, and it was far too much of an info dump to give me anything immediately useful, but there are certainly things to think about.)
This silly little joke idea I had keeps getting bigger.