My DVR recorded a bunch of old episodes from the season Katie and Tom got married, I think last week? I rewatched their wedding episode again today for the first time since it aired.
Anyway, during the reception, Lisa asked Katie and Tom for the marriage license, saying that she had to sign it. Tom produced it right away and Lisa sat there and signed it. She then gave it back to Tom for him to mail.* So, if it got lost, it was after the wedding, not before.
*I thought that part was weird, because I’ve been married (twice 😬), and neither time did my officiant give the license back to me to mail. It might just be my state (Illinois) or county (Cook), but I think it’s supposed to be the officiant who mails it back?