Accidentally sent unsupported ERC20 to ETH wallet at Kraken

I am not looking to be judged or told that I did something wrong, but yesterday I sent some USDP (Paxos Dollar) to my ETH wallet at Kraken. Immediately I realized they don't support USDP, and of course it never showed up in my account.

I can see the USDP on Etherscan. I put in a ticket at Kraken and they quickly sent me back a response that there is nothing they could do and they marked the case as "resolved." Really?

This isn't life-changing money, but it is enough for me to be mad at myself for sending the crypto to Kraken without remembering that they don't support it.

Is there anything I (or they) can do? Is that money just gone forever?