Overwriting Parenst Theme Functions

I have an issue which is most likely caused my lack of coding knowledge.

My parent theme include the following function within framework/register_public.php.

function simple_breadcrumb_case($der_post){
		$markup = $this->options['before'].$this->options['after'];

		if(is_category()){
			$category = get_the_category();
			$i = $category[0]->cat_ID;
			$parent = $category[0]-> category_parent;
			if($parent > 0 && $category[0]->cat_name == single_cat_title("", false)){
				echo get_category_parents($parent, TRUE, $markup, FALSE);
			}
		return __("Archive for Category: ",'dt_themes').single_cat_title('',FALSE);
		}
	}
}

I want to change the return at the end to:

return __(" ",'dt_themes').single_cat_title('',FALSE);

but obviously I want to do this in a child theme so future update aren’t overwritten.

I have duplicated the file into the same path as my childtheme and altered it. That didn’t work.

Then I read that you have to declare a new function in your child themes function.php, so I created:

function childtheme_simple_breadcrumb_case(){

}

Then change the instance of simple_breadcrumb_case in the child theme to the new function childtheme_simple_breadcrumb_case. Whilst altering the return(); to include the changes I want.

This is where I get stuck I am not 100% how I overwrite the parents themes functions.