I keenly remember embarrassing moments where I made myself look like a fool or did something generally stupid as far back as kindergarten. Some of them are so petty that there is no reason to actually remember them at all, but there they are. It's been a problem when assessing "Is this important enough?" Probably not, but my brain is still pretty clear it's going to do that whether I like it or not.
I think it depends - I mean, obviously people can't really decide what they remember and don't. But the point of the question is to assess how much energy you should be putting into something. Embarrassment is one of the strongest negative emotions - Same with guilt and shame. If you're embarrassed about something in general, it means that it might've been a "learning" moment for you. Whether or not you actually remember it in the future doesn't really take away that power, and therefore it's something you
should invest your energy into.
I view it in the sense of - Does this fight that I'm having with this family member - Am I going to remember it? Unlikely, especially if there's not a lot of strong shame aspects to it. Just a fight about some food being eaten isn't on the same level of feeling like someone you cared about is making you feel ashamed. Does that make sense?
It's not that it's "important" enough really, it has to do with in this very moment, at this very moment in time, do you think it's a good investment to feel like a nervous wreck (or sad or whatever) over something like this? If you think it is, then you should. Even if it's deemed "minor" to yourself or by others.