Furthermore, Google News is a big player and they probably don't get a lot of "signal" from their viewers. Google is all about algorithms. It certainly counts clicks but it also, certainly, counts the number of readers who divorce news outlets.
The generic algorithm is likely to start skipping stories from a given source after enough clients actively turn that particular source off. That starts biting the ad revenue of the news source in big way.
This is how to do it.
Click on the three, vertical dots and you pull up a menu that looks like this.
Clicking on the middle choice hides all stories from that source.
Verifying your work
You can verify that you successfully turned off that particular news source by going to the main menu (left column) and going to the bottom of the list where it says "Settings"
If you click on Settings you will get a menu that looks like the image shown above.
If you then click on Manage you will generate a screen that looks like the image shown below.
I have no clue who turned those sources off.