In your template.php, we will add the following code. It is a theme override of theme_apachesolr_facet_link()

In the following example, we check for a facet called "Tip" and exit out early before it is themed. You can add your own code here and modify the arguments as necessary.

// Theme override of apachesolr_facet_link
function [your_theme_here]_apachesolr_facet_link($facet_text, $path, $options = array(), $count, $active = FALSE, $num_found = NULL) {
  // Don't theme any facet text called 'Tip'
  if ($facet_text == 'Tip') return;

  $options['attributes']['class'][] = 'apachesolr-facet';
  if ($active) {
    $options['attributes']['class'][] = 'active';
  }
  $options['attributes']['class'] = implode(' ', $options['attributes']['class']);
  return apachesolr_l($facet_text ." ($count)",  $path, $options);
}