Implode Taxonomy to hide parents?

You can check if the resulting term has any children before adding it to the array:

$terms = get_the_terms($wp_query->post->ID, 'propertytype');
 $props = array();
 foreach ($terms as $term) {
    $hasChildrenTest = get_term_children($term->ID, 'propertyType');
 if ($term->parent) { 
    if (empty($hasChildrenTest) && !is_wp_error($hasChildrenTest)) {
         $props[] = $term->name;
    }
 }
 echo implode(', ', $props);

ps: the if($term->parent) test might become unnecessary after this. Check if you really need it.

edit: my mistake -> it should be empty $hasChildrenTest instead of !empty $hasChildrenTest so if the term has children it doesn’t get added.