After hacking, they were banned

With mail correspondence with the Steam Support confirming that your account was hacked, and that the ban occurred while your account was hacked, you should be able to contact the BattlEye support to prove your innocence. Again, nobody on these forums can help you, all communications has to go through the Steam and BattlEye supports. The Steam reply that you have been banned by developers is due to them differentiating between Steam and developer bans, while our developer-side bans are handled by BattlEye.

Closing the topic.