I can be wrong but what I understand here is that images may be loading on a secure site (https) but their links are (http) What I understand from that is the server from where the post is published should be configured to fully support https first.
EDIT: but that doesn’t looks like the case, I visited the site and both WP and Discourse are configured to load over SSL. What needs to be seen is how have you configured Discourse WP plugin.