It is possible to block messages from reaching your user's inbox by creating a system-level filter for the entire server. Use the following guide to learn how.
Login to the server via SSH as the root user
Create the filter file with the following command:
Edit the file with a text editor of your choice and put the following contents within:
if ("$h_subject:" contains "example subject")
if ("$h_subject:" contains "another example subject")
Edit the contents of the file so that it blocks your desired subjects
Login to WHM as the root user and navigate to the following location:
WHM >> Home >> Service Configuration >> Exim Configuration Manager
Click on the Filters tab
Verify that the custom filter that you just created is enabled, or disable the filter if you desire to do so.