Wordpress - image_size_names_choose filter doesn't show

No, that seems to work right. You could test it by doing

<?php echo get_the_post_thumbnail('grade-image'); ?>

try this.

add_image_size( "grade-image", 320, 300, true );
add_filter( 'image_size_names_choose', 'my_custom_sizes' );

function my_custom_sizes( $sizes ) {
    return array_merge( $sizes, array(
        'grade-image' => __('Grade Image'),
    ) );
}