It's definitely suspiciously cheap, but I think I have the reason.

The dollar store I visit only sells >$1 electronics when they get them surplus from other stores that couldn't sell them. That's why I still sometimes find weird devices there using outdated (30 pin, miniUSB) plugs.

In this case, the Bluetooth IC (NRF 8001) itself costs over $2, and that's just one single part needed to make this work. Because of that, I think that the original product was probably around $10 but didn't sell, and as such ended up at the local dollar store for $2. They couldn't have possibly originally sold this for $2 because one single part already costs ~$2.20 or so.

Unfortunately if there was software it no longer exists, as the website this thing linked to isn't up. That also kind of makes sense, it was probably sitting in the back of some Kmart or something for years before getting sold at 1/4 off to the dollar store for resale, so the original company supporting these devices could have gone out of business. Or, I am clueless and just can't find the software haha. With only one button and no labels it would be difficult to even get it to pair without instructions.