If you like to delete shown post in the NewsBar, there are two ways you can use.
WAY 1 (context menu):
WAY 2 (cumulative):
Recall that posts from one source are grouped together inside NewsBar and caption of that group includes two buttons shown in the screenshot below. By using those buttons you can mark all those grouped as read or delete them at once.
Keep in mind that posts loop inside NewsBar and based on your preferences it may be shown once or more. Deleted posts are removed from NewsBar and not shown again at the next loop, if there is.
There is also automated way of deleting posts, as described in related help topic listed below.