A family of Microsoft word processing software products for creating web, email, and print documents.
Whether we like it or not, cloud based services are here to stay. By refusing to enable what Microsoft refers to as Connected Experiences you are denying yourself the availability of these features:
Connected experiences in Office
There seems to be some concern about Microsoft violating the privacy of their users but that just isn't how it works. Users are far more at risk by using email & browsers as well as other practices which subject them to exposure. If you haven't already done so, examine the links at the bottom of the Manage Connected Experiences Preferences pane in addition to the link above.
You also have the opportunity to use Help> Feedback to submit the issue to the developers. Don't expect a personal response but comments submitted in that way do go directly to those who produce the software. Enough demand just might make the popups go away once they've done their job.