OK, assuming your URL is exactly what you have there might be some issues.
It should just be /html/com_k2/ inside the actual template you're using.
Then, create a subfolder ('grid', for example) and copy in only the views that you want to override.
So if you need to override the category list view, you'll need at least category_item.php and probably category.php.
If you need to override the item, you'll need item.php.