This feedback is really useful; we've struggled to nail the process as it is generally very cumbersome having to sign in & out of Twitter accounts (but it's the most secure way, as opposed to XAuth, which would be a possible alternative).
The key thing here is showing the user they have a new invite/notification, which we will add ASAP.
The key thing here is showing the user they have a new invite/notification, which we will add ASAP.