The answer from @the_dramatist is probably the simplest if that's all you want to do, but you can remove it completely and customize everything else as well by creating your own comment template.
As Ethan mentioned in the comment on your question, every theme is different, meaning that most themes have a comment template that is inserting this or are using the default template. If your theme has a custom comment template already, just edit that one otherwise it's using the default comment function which includes the comment author says text.
If you have anything else besides that that you'd like to customize you're better off creating your own template or function for this. You can create a [custom callback or custom walker.
Then you'd use wp_list_comments() to output your new comment template.
So basically here's the process of doing this with templates:
2) Create a
comments.php file and call your new function:
'walker' => new Walker_Comment()
<?php wp_list_comments('type=comment&callback=format_comment'); ?>
3) Output your comment template on
<?php comments_template(); ?>