This invoice says "underpayment", which makes me think you just didn't send enough bitcoin. If this invoice came from TER then that makes perfect sense. In this hypothetical case, you've underpaid for your VIP service, and TER sent you bitcoin back as a refund.
If you read the bitpay fine print under the bitcoin payment option, you'll see that the rate you're getting is only good for 15 minutes, so provided you sent the right amount of coin, the value of it could have changed, and if you waited longer than 15 minutes to fire off that transaction you likely had this happen.
I've used bitpay in the past, and have always made sure to have the transaction from my wallet ready to go, hit the bitpay button to get the barcode, copy/paste the address and amount into my wallet and hit go as quickly as possible, to avoid exactly this.
It's important to realize that there is no such thing as "accepting" a payment with bitcoin. If the transaction is confirmed by the network, whatever bitcoin address you sent the funds to now has your bitcoin. It seems like you have a fundamental misunderstanding with how this process works.
You're also not getting any additional privacy by using a NATO based bitcoin wallet provider, because they have to keep records of who buys what and sends it where. In order to get the anonymity, you'd have to send it to a wallet you own and control, then to TER. Because this intermediate wallet isn't auditable, it's impossible to prove it was you that sent TER the coins.
The way you phrased your question was that "bitcoin" had sent you a refund, when in fact TER had sent you a refund. That's what threw me for a loop, not the sauce. I don't usually drink while the sun's still up, unless I'm somewhere tropical, then all bets are off.