Exclude blog category from archive only

Hi there
I’m using a theme where the top sliders are posts within a category (Home Slider), but don’t have any accompanying text as they are generic and don’t relate to any specific content.
The problem is, they show up in the archive list (bottom right-hand sidebar of site), and of course when you click on the link, it only shows an image of the slider, nothing else.
How can I exclude these sliders from the archive listing? I’ve tried some php snippets in functions.php based on category ID, which removes the sliders from the archive, but ends up removing them from the home page too!
The theme author is no help at all (bk-ninja Gloria theme) and simply says, ‘The blog archive query is controlled by WordPress Core, it’s something you have created at a moment, so I think there is no way to remove it from the archive query. I think it’s not an issue.’
Any help gratefully accepted! James.

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