I recently had an open ticket with Logmein support (my first interaction with them), and I got a one-off email from a Logmein support agent, and he shared the following link to close the case:
https://cases.mylogmein.com/close-case?id=
After the "id=" in the url there was a unique string of numbers. He emailed me from "so I assume this was legit, but I wanted to make sure.
Thanks in advance.
(Edited email address in comment to prevent others using it by mistake and expecting a reply - GlennD)