hash: What happens if I send an XRP transaction to a blank TAG when I'm supposed to send a specific TAG?

I sent XRP to a blank TAG while I was supposed to send it to the TAG of the change. The address is the exchange but the TAG was left blank. The exchange says they can not recover the money.

What happened with the money? Is it theoretically possible for the exchange to recover it? As I understood, a blank label but with a correct address will send the money to the exchange but not to anyone's account.

ps: I just realized that "crypto" means cryptography, not cryptocurrency, could someone move this to a better forum?