Remove current_page_parent from posts page link in WordPress nav menu

I assuming you’re using wp_page_menu() or wp_list_pages(). If so, then what you need to do is hook into the page_css_class filter, e.g.,

add_filter ('page_css_class', 'my_func', 10, 5) ;

function
my_func ($classes, $page, $depth, $args, $current_page_id)
{
    if (/* test condition */) {
        $classes = array_diff ($classes, array ('current_page_parent')) ;
        }

    return ($classses) ;
}

where /* test condition */ is where you’d put your logic to decide when that class should be included.