Hi there, Jared.
The reason why you are getting the Invalid invite link is due to the fact that the Invite URL has either been disabled from the admin's end or a new one has been generated (causing the one you had to be obsolete):
Should there be a need to have your account created in HipChat, please reach out to the group admin to refer either of the following steps mentioned in the Invite people documentation:
Let me know how it goes on your end.