Insecure content

We moved our site to a new host (SiteGround) and after we finished getting the site set up, we purchased and they added an SSL certificate to the site.

However, when you visit the site the security message in the location bar says that there is content on the page that is not secure (such as images).

The tech as SiteGround suggested I install and run this plugin:

I'm hesitant to run it on the live site. After reading the docs for the plugin, it says there could be a problem using it with responsive images (we're using the Divi theme which is responsive).

I was just wondering if you had any experience with the plugin, and if using it is the recommended solution for fixing the problem. Thank you!