Remove comment sidebar when no coments

Hello,

I am hopeful for a simple solution to this one if anyone can help.

My website alwaysremembered.org is a memorial website set up as a multisite with new tributes being given a predefined WP setup with set pages managed through the frontend via a modal box.

One of the features I have is a tribute section where someone can leave a tribute (comment). The latest three of these are displayed on the front page. I would like to stop that from showing when there are no comments.

This is an example site

As I said the simpler the better with this, preferably without the use of a plugin. Is there anything on the sidebar.php that I could change?

Appreciate the help, let me know if you need more info,
Ben