Change how links are handled on front page

Thanks for a great and really customizable theme, really enjoying working with it so far!
My client doesn’t like how links are handled on the feature images on the front page, so i’ve disabled a few bits – but they want to be able to link to the posts the feature images are coming from.

Could you point me in the direction of what would need amending in order to achieve this?
I imagine it’ll be an amendment to the HomePage template php file, which i’ll embed in a child-theme?

Any direction or advice would be greatly appreciated!

The page I need help with: [log in to see the link]