I am filing this as a sibling issue to #3995

In the WP dashboard, the "Welcome to WordPress!" block can be dismissed (per user), via a link at the top-right:

Screen Shot 2019-08-26 at 5 43 49 am

We should introduce such a feature as well; perhaps in a way that it can be reused by other blocks too.

GitHub Link: 
https://github.com/backdrop/backdrop-issues/issues/3996
GitHub Issue #: 
3996