That's very risky and shady now. There handling fee is very high while the service that will gonna do is just to input there private key on a different blockchain. Asking additional expensive fee instead of just deducting it to the balance that they are being held is very scammy. At first I thought that there support is just pulling some shady offer to you but now I think this really there official policy on handling this things.

I suggest to post this issue including the Screenshot of there conversation on twitter and tag them. Contact this guy @RealCryptoV on telegram. He is famous for exposing scammer in crypto so that Bkex will take seriously your concern.

This is his telegram news channel: https://t.me/CryptoVigilanteANN