For some time now I keep seeing this on most of the SE sites I visit:
While I admit that this is a useful piece of information, I still want to find out how many more days will I be seeing it?
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That prompt will remain until you log in and minimize it, like mentioned in the announcement of said prompt:
If you don’t belong to any teams, there will be a prompt to start a team, which can be minimized.
To do so, press the X in the upper right corner:
Again, you need to be logged in to do this. If you're visiting anonymously, you're out of luck and will probably keep seeing this for as long as the company wants to show it. But once you've done that, all that will remain is a single link: