I've just migrated from WSS 3.0 to Sharepoint 365, and on the 'home' page, there is a link ("Product Services") in the top navigation bar that is not editable. I've checked every setting I can think of and can't figure out how to get rid of it. If I just try to edit links, that link disappears and isn't editable. The link isn't present on any of the sub-pages like all the others are via inheritable permissions, but it's driving me nuts that I can't get rid of it. Any help is appreciated.
I experience this problem too. In my case, it is due to caching. I try opening SharePoint online using different browsers (Firefox and Edge) and the recent changes in Global Navigation takes effect in different browsers that I have not used to open SharePoint Online before. Clearing the browser cache solves this issue in my case. I hope this helps others.