My point is that perhaps the OP’s wife mistook a simple greeting as inappropriate. My story with me greeting a “strange woman” can be misconstrued by a strange woman.
Chesedname, I should hope you don’t run to file complaints each time someone from the opposite gender greets you while walking by you.
All I am suggesting is that they should approach their LOR before taking further action. As there are people who perceive any questions as inappropriate.
Another note, I find it amusing that she would potentially have the guy fired, but it isn’t severe enough to at least avoid the store due to convenience.