Oh, I get it now.
Even if you have installed the Friends plugin, people can invite other on-line users by clicking the "Chat now" button if they go to the "Members" page of your site.
And you are right, the possible solution to hide this button is change the privacy settings. You can set as default the "Friends only" value for the option "Who can invite me to chat" on the Privacy setting page.
It is a custom code modification.
You need to edit /ow_plugins/mailbox/classes/event_handler.php file.
Find this code:
if (in_array('chat', $activeModes))
{
$action = array(
'key' => 'mailbox_invite_to_chat',
'pluginKey' => 'mailbox',
'label' => $language->text('mailbox', 'privacy_action_invite_to_chat'),
'description' => '',
'defaultValue' => 'everybody'
);
Change the value "everybody" to "friends_only" value.
Once the changes are made don't forget to clear the browser cache and the smarty cache (DEV_MOD, use this manual:
https://docs.oxwall.org/plugin-tuts:enable-debug ).