Why are workflow notifications that I acted on still in the global header and home page?

If you acted on the workflow task elsewhere, the notifications remain until after the next scheduled run of the Synchronize Notifications in Global Header process.

For example, you approved a task through email or the Worklist: Notifications and Approvals work area. The notifications list in the global header and the Things to Finish section on the home page won't immediately reflect that change to the workflow task. The same goes for the Notifications page that you can open from the notifications list in the global header or from the Things to Finish section.