I’ve always been confused about how to handle this situation, and it happens mainly in relation to my family members. For example, I’ll be at a grocery store, and I’ll run into someone who knows me and my parents. After we exchange pleasantries, they’ll say something like “Tell you mom I say hello!” Should I take that literally and tell my mom that person says hello or is it one of those weird social things where people tell you do something, but you don’t really do it?
I think that it’s the kind of thing where it’s ok if you do it, and ok if you don’t.
Like, for instance: "Oh, by the way, I ran into Sarah in the store. She says hi.“
I’ve found that it’s often difficult to pass on the greeting. Sometimes there’s no natural way to do it; sometimes there just isn’t a point in the conversation you have with the person where passing along the greeting would feel on-topic.
And the longer it’s been, the more weird it gets.
It’s ok not to pass on the greeting, and probably better not to if it’s been more than a day or so.
If you don’t pass on the greeting, no one is likely to mind.
The exception is if it’s someone you haven’t seen in a long time and seeing them was generally surprising or otherwise notable. Because then passing on the greeting gives the person you’re passing it to meaningful information. Eg:
"Guess who I saw in the store? Sarah! I haven’t seen her in ages! She says hi.”