The Claude Code client adds system prompts and makes a bunch of calls to analytics/telemetry endpoints so it's certainly feasible for them to tell, if they inspect the content of the requests and do any correlation between those services.

And apparently it's violating the terms of service. Is it fair and above board for them to ban people? idk, it feels pretty blatantly like control for the sake of control, or control for the sake of lock-in, or those analytics/telemetry contain something awfully juicy, because they're already getting the entire prompt. It's their service to run as they wish, but it's not a pro-customer move and I think it's priming people to jump ship if another model takes the lead.