The email notice that bounties have ended and are entering the grace period as well as the inbox notification seem to happen before the bounty period is actually over.
Several similar requests marked as bugs have been turned away as "by design", but I believe this is kind of silly. This keeps coming up and should be fixed.
If the timing mechanism isn't going to get fixed so that it actually sends notices at a consistent time in relation to the end of the period, then at least update the copy. If you don't know whether the period is up or not, don't pretend like you do. Instead of "has completed" say "completes today at HH:MM UTC" and let the user figure it out when they follow the link. But even if the timing mechanism doesn't know ahead of time you should be able to query the end timestamp and regenerate the string based on the current time. There shouldn't be any reason the notification can't read just like the page does at the time the notification is sent.