The Pith Helmet was a staple of Banana Republic from the very beginning. While it was likely a popular novelty buy, the BR helmets were authentic Indian imports. They were also something that people seem to hang hung onto, as they are surprisingly common on eBay, where you will see a few variations in interior fabrics and labels. Most of them simply say “Made In India” and don’t have a BR label, but there was at least one that was manufactured with the circular parrot logo. See gallery below. The hat box was optional, I suspect.
Thanks to JT for pictures of his with the price tag still attached. The Parrot version is in my own collection.