Gas costs are not something which the platform could keep - they are for maintaining the Ethereum blockchain network. So every transaction costs gas, regardless of who sends it.
A refund can be one of three types: 1) you pull the assets back or 2) the platform sends them back or 3) it's done automatically with some other transaction.
If you are meant to pull the refund, then you pay for the transaction cost.
If the platform sends the refund, then they pay for the transaction cost.
If it's automatic, then whoever initiates the transaction which triggers the effect, pays for the gas. This is probably the most likely scenario, I'd say: whenever someone outbids you, the same transaction automatically refunds you your assets back.
Anyway, it depends on the platform implementation. And you don't get your transaction costs refunded.