So I was able to fix it. In anr-captcha-class.php I changed:
if ( function_exists( 'wpcf7_add_shortcode' )) {
wpcf7_add_shortcode('anr_nocaptcha', array($this, 'wpcf7_form_field'), true);
add_filter('wpcf7_validate_anr_nocaptcha', array($this, 'wpcf7_verify'), 10, 2);
}
To this:
if ( function_exists( 'wpcf7_add_form_tag' )) {
wpcf7_add_form_tag('anr_nocaptcha', array($this, 'wpcf7_form_field'), true);
add_filter('wpcf7_validate_anr_nocaptcha', array($this, 'wpcf7_verify'), 10, 2);
}