Every Ethereum client (whether you are a staker or not; you can run a full node without staking!) recognises slashing transactions, and debits the balance of the misbehaving staker in their records.

In other words, the blockchain; in the same way that it's not _miners_ / stakers who process transactions on bitcoin or ethereum ; miners / stakers only decide _ordering_ but everyone who runs an Ethereum client is processing and verifying every transaction; the same way your browser checks a TLS certificate.

So, since the client is debiting the slasher, then THAT transaction is an ether transaction on the chain, and it gets reviewed just like any other transaction as well?

Thanks for your answer!

To answer "who removes the ether":

The value in a staking account is calculated on the blockchain as "amount staked minus slashing penalties", and this violation is automatically recorded as a slashing penalty, so the answer is "everybody"