Remove Archive Headline and Archive Intro Text fields on category and tag archive pages in WordPress Admin with Genesis framework

It’s not because of the archive_box in cpt-archive-settings.php but because of genesis_taxonomy_archive_options in genesis/lib/admin/term-meta.php.

You can remove it using if you place the following in child theme:

remove_action( 'admin_init', 'genesis_add_taxonomy_archive_options' );

Update:

Those settings are appearing because of the action genesis_add_taxonomy_archive_options attached to admin_init hook.

add_action( 'admin_init', 'genesis_add_taxonomy_archive_options' );

Which again is like this

function genesis_add_taxonomy_archive_options() {

  foreach ( get_taxonomies( array( 'public' => true ) ) as $tax_name ) {
        add_action( $tax_name . '_edit_form', 'genesis_taxonomy_archive_options', 10, 2 );
    }

}

So basically it is hooking to {$taxonomy}_edit_form.

Another Way

The following works even if it is used in plugin/theme.

add_action( 'admin_init', 'wpse_add_taxonomy_archive_options', 11 );

function wpse_add_taxonomy_archive_options() {

    foreach ( get_taxonomies( array( 'public' => true ) ) as $tax_name ) {
        remove_action( $tax_name . '_edit_form', 'genesis_taxonomy_archive_options', 10, 2 );
    }

}

Thanks to @Mark.