It is not worth it to reply to a mail.
If you think you are in your right. Just rebook, and claim again.
However, if I understand your case l correctly, the additional person charge is indeed excluded in the terms and conditions, so resubmitting unfortunately won't be of much help.
Yeah I just figured this out. The first person that replied said nothing about that, they just made up some stuff that both had to be lower.. So I was ready to fight that. This time around the person actually pointed to the "additional guest charges are excluded from the guarantee" portion of the T&C.
Damn. I totally missed that