If I connect with others via StreetPass and then I edit my Mii's appearance, will they see the change?

I didn't pay much attention when I was creating my Mii, and never cared too much about it or considered it important.

Yesterday I met someone via StreetPass for the first time. Everything went normal, but after seeing my Mii carefully, I wasn't too convinced about its look, so I immediately edited it and ended up satisfied with the new result.

Will the person I connected with via StreetPass be able to see the change on my Mii or would I have to connect with them again so they could notice?

No, the person you connected with in StreetPass will not see your updated mii UNTIL you can manage to connect with them again. This is because the 3DS StreetPass doesn't use the internet, and has no way of connecting unless you are in the radius of the other person's StreetPass, as it does not update live. As a matter of fact, Your mii won't update until the other person connects with another person before he/she connects with you again. This is because the StreetPass will not attempt to connect with the same device twice in a row in such quick succession.