As I said, it's more like an internal departmental memo. It serves a purpose internally, but trying to use it outside of that context is mostly a category error.

The document itself may have an internal purpose, but there is no legitimate purpose served by calling it a warrant. That serves purely to mislead.

That's not correct. It's a "warrant" in the literal sense: it authorizes federal immigration agents to detain someone for civil immigration violations. Since they're not judicial warrants, there are constitutional restrictions on how they can do that, which I enumerated in my previous comment.

The game ICE is playing takes advantage of the exact misunderstanding you've described - that anything called a warrant must be a judicial warrant. That's not the case, they're just exploiting people's bad assumptions.