Removing \\\ from Saved Data

You can change the " signs to " automatically using PHP’s htmlspecialchars() prior to your update_option() call:

$post_client_template = htmlspecialchars( $post_client_template );
update_option( 'contact_record_client_template', $post_client_template);

If you need to change ' characters as well, use this:

$post_client_template = htmlspecialchars( $post_client_template, ENT_QUOTES );
update_option( 'contact_record_client_template', $post_client_template);