Usually do not try to redo an interview answer afterward. A thank-you note is for appreciation and continued interest, not for submitting a replacement response.

Post-interview corrections can draw attention to a weakness and create information the interviewer did not ask for.

If the omitted fact is genuinely material, such as correcting a factual error or required eligibility detail, contact the recruiter. A stronger anecdote is normally not material.

Write down the better example and use it in future interviews. Let the original interview stand on the performance you gave.

I had the same concern before recruiting. Once I practiced the exact situation a few times, it felt much less awkward.