The additional network cost included in your invoice total covers the cost of BitPay's UTXO sweep for your payment. You can learn more about the reasons for this additional fee here: https://blog.bitpay.com/network-costs/
This fee is used for BitPay's UTXO sweep, so it is not returned with refunds.
We strongly recommend that you send a miner fee with your bitcoin payment. Miner fees are given to the bitcoin "miner" (specialized hardware that processes transactions on the Bitcoin network) that appends the transaction to the Bitcoin blockchain. These miner fees are not BitPay fees, but they do increase the likelihood that your transaction will confirm on the Bitcoin network in less time.
A simple way to ensure that your transaction includes an appropriate fee is to adjust your bitcoin wallet settings to include a dynamically-calculated fee. Our bitcoin wallet BitPay includes this setting option, which will help ensure that your transaction confirms normally even at times of high Bitcoin network traffic.
You can find more information about bitcoin miner fees here: https://support.bitpay.com/hc/en-us/articles/115003393863-What-are-bitcoin-miner-fees-
Refund Miner Fee Cost
If you underpay or overpay an invoice and initiate a refund to yourself, BitPay will deduct the miner fee cost of returning the payment from the total refund amount you receive.
If you are a BitPay merchant and issue a full refund to your customers, the miner fee amount will be deducted from your merchant ledger balance. The deduction will be added as a separate entry in your BitPay ledger after the refund is executed.