If you have absolute URLs (http://..../foo.jpg) saved in documents or a database or something like that, you would need to rewrite them to be protocol-relative or just https:// .
Surely the GP wouldn't have asked the question they did if their https site was already broken...
You could do this quite subtly as a way to influence people by making certain figures appear more sinister.
These warnings tend to get tougher over time, so what's grey now may be red next year.
1. https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Co...