You can't.
You can't really remove anything that has been made public. You can try but odds are there is a copy somewhere.
For bitcoin: if everyone was cooperating you could update the protocol to replace that block with a version that had the desired information removed, however this block and its replacement would require special verification because the normal rules will obviously fail (because the normal rules forbid change).
Although miners can collude to replace data, there are still copies of the prior data from people who can't contribute to the collusions and it would be major news at that point in time. Crisis of confidence have occurred in these systems and every major service has managed them before (typically by either rejecting deposits and withdrawals client side, or extending the amount of time necessary to determine if the content of a block stays where it is), and then the chain continues as normal when the disruption is gone (time to check if block content stays drops back lower).
It's no different than any other software; it has to gradually earn confidence over time. Major math flaws were found in Zcash and more recently ECDSA threshold signatures and they had to be patched. Likewise understanding of cryptoeconomics has evolved (see selfish mining and MEV as examples) and will continue to evolve. It happens.
How do you delete data from the blockchain?
You don't put the data on the blockchain in the first place; you put a pointer. This doesn't solve all cases but it's better than nothing.
- Who runs the ledgers and what guarantee is there aside from cryptographic smoke that the entities/corporations running the ledgers can't collude? This gets into the question of independent cryptographic audits and looking for mathematical back doors. How can one know with certainty that one entity can't make subtle manipulations to this systems/markets?
- How do you delete data from the blockchain? Let's say someone decides to use blockchain for identity management. Some day a court agrees that a person needs to be protected under witness protection but their identity is in the blockchain. How do you remove it? Not revoke it, but completely remove all traces of it?