How can I get the BattlEye Halo?

Please don't try to get this item!

In cases where BattlEye has accidentally banned players for false positives they have given out this item as a gift with their apology. (along with unbanning of course!)

From the item description:

"Unfortunately, due to to a false positive you were accidentally banned by BattlEye. We are very sorry for this big inconvenience and will do our best to prevent something like that from happening again in the future. As a form of compensation, you get this unique item from the game developers." -BattlEye Team

What if I was unbanned but didn't get the item?

If you hadn't played the game within 30 days before the unban it's possible the item was unable to be added. Steam requires that the game be played recently, presumably as a precaution against game developers using items as an advertisement to every player on the platform. In this case sorry to say there isn't currently a way to recover the item (yet).