I am just now configuring My News on my tablet. Each news source tile has a setting menu on the far right next to its name (3 vertical dots). Pull that down by clicking, and select "Remove" from the menu, if you do not wish it any longer. Mine came with 12 pre-configured tiles, which I turned off way.
It is easy to add them back from the "Featured" list if you decide later to return to that news source.
UPDATE:I'm not seeing any direct removal of stories of the removed news sources when I first return to "Read Now", but I believe I must click through to expire the stories already presented, and then refresh to have the content cleared.
UPDATE2: Well, that's annoying. There could still be a number of items in the queue from the first opening of the app with pre-selected news sources. I may have to click through them all to see when my preferences will be adopted.