Deleting contexts in Drupal 7

When removing contexts, use context_load to retrieve context object from the database, then context_delete to remove it.

A specific example:

function example_update_7001() {
  // 'example_one' is the value at /admin/structure/context in the Name column
  $contexts = array('example_one', 'example_two');
  foreach ($contexts as $context_name) {
    // load the context from the DB
    $context = context_load($context_name);
    // context_load returns FALSE if the context doesn't exist
    if ($context) {
      context_delete($context);
    }
  }
}

You can also check the module is even enabled with module_exists('context') around those lines.