Display Child Taxonomy on Posts without Parent

Hello! I’d love some help with this. =)

I’d love to remove the parent terms of a custom taxonomy from displaying on posts.

Currently it displays, Parent, Parent 2, Child but I would only like to display the Child.

What is the correct php for doing so?

I found this code, but I don’t know how to modify it to only show the final child.

<?php

$terms = get_the_terms( $post->ID, 'From' );
if ( !empty( $terms ) ) {
    $output = array();
    foreach ( $terms as $term ){
        if( 0 != $term->parent )
            $output[] = '<a href="' . get_term_link( $term ) .'">' . $term->name . '</a>';
    }

    if( count( $output ) )
        echo '<p><b>' . __('Categories:','om_theme') . '</b> ' . join( ", ", $output ) . '</p>';
}
?>