How do I remove the More Articles on the Category Blog Layout page?

To fix this issue and remove "More Articles..." you will need to edit the .php file. There is no way to remove these words internally within Joomla.

You must be comfortable with editing Joomla files directly. I usually import the file into Dreamweaver, but there are many ways to get the file code.

Go to the file: components/com_content/views/category/tmpl/blog_links.php file

It is a small file, and you will notice "More Articles..." within the code. If you want to remove the words, just delete the characters leaving everything else. You can also change the text instead of deleting it. 

Save the file, and test out your Category Blog Layout page. It should be fine now.