Pluck single parent category from get_the_category

You can check the category 'parent' arribute, and if is 0 the category is a parent one.

I’ve also noted some things on your code:

1. When the is is passed get_the_category is unused, but it is called anyway
2. You use get_the_category assuming function are called in the loop, but there is no check for that
3. If, for any case, get_the_category return no categories, your function thrown errors
4. Before inserting retrieved values inside html shoul be escaperd with esc_* functions

I rewrote your function considering all those things and adding the check for parent category:

function thb_DisplaySingleCategory($boxed = true, $id = false) { 
  if ( (int) $id ) {
    $cat = get_category($id);
    if ( ! empty($cat) ) {
       $backup = $cat->term_id;
       if ( $cat->parent == 0 ) $id = $cat->term_id;
    }
  }
  if ( empty($id) && in_the_loop() ) {
    $id = '';
    $categories = get_the_category();
    if ( empty( $categories ) ) return;
    while ( empty($id) && ! empty($categories) ) {
      $cat = array_shift($categories);
      if ( $cat->parent == 0 ) $id = $cat->term_id;
    }
  }
  // if no parent cat found, but a not-parent cat id passed to function use that
  if ( ! (int) $id && isset($backup) ) $id = $backup;
  if ( ! (int) $id ) return;
  $name = get_cat_name($id);
  $url = esc_url( get_category_link($id) );
  $wcolor = $boxed ? 'background' : 'color';
  $class = $boxed ? ' class="boxed"' : '';
  $color = GetCategoryColor($id);
  $frmt="<a href="https://wordpress.stackexchange.com/questions/119997/%s"%s title="https://wordpress.stackexchange.com/questions/119997/%s" style="%s:%s;">%s</a>";
  return sprintf( $frmt, $url, $class, esc_attr($name), $wcolor, $color, esc_html($name) );
}