I'm guessing you mean the notification in the Confluence Workbox?
Workbox notifications will be automatically deleted after 2 weeks if you've read them, and after 4 weeks if you haven't read them, but there's no way to manually delete them.
This is a question I get a lot when I'm training people on Confluence, and I've never been able to find an answer. There isn't a ticket in requesting the functionality either (at least, not that I can find).
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