Is it damaging to let someone’s misunderstanding of what you’ve said go uncorrected? Depends on what you mean by damaging, but it’s unlikely to ever be a good thing, except in the most mischievous of cases.

As wonderful as it might be for your opinion of yourself to be completely independent of what others think of you, humans are too social and capable of abstract thought for this to be the case. If you know someone sees you in a negative light as a consequence of their misunderstanding of something you said or asked, it can weigh you down. This problem is compounded when more people are around to misunderstand what you’ve said. But the most damaging thing about not correcting their misunderstanding is that it could lead you to become comfortable in keeping your silence when similar situations inevitably occur in the future. On the other hand, there’s a limit to how much effort should be expended on correcting a person’s misunderstanding.

When they think they know what you mean, some people are like stubborn trains unwilling to switch tracks. Or it might well be your own fault, your fumbled words which led to their misunderstanding in the first place are now digging the hole deeper in spite of your efforts to do the opposite. And there’s a limit to how much people can take. For example, in a classroom where you’ve asked the Prof a question and they’ve addressed the question they thought you asked but didn’t, the rule of thumb is this: if you can’t articulate what you meant within 2 back and forth exchanges with the Prof, then you deserve to be misunderstood, however unpleasant that might make you feel, especially if the Prof believed you were asking about something sickeningly obvious.