The terms of service are between Anthropic and one of their subscribers. So Anthropic can maybe cancel their contract.

This doesn't affect what copyright law allows or does not allow.

Also I think Anthropic very much suppports gathering data by whatever means possible. That should work both ways.

It does make a difference. If this text was generated by the LLM, then by those same terms you are allowed to publish the data. But given that it is reverse engineered, you are not allowed to do so.

Note that even in the normal case, there are restrictions. You'd have to validate that the generated output is not copyrighted. Which in this case may not be trivial.