Remove a device from the bluetooth menu?

I was messing around with my bluetooth this morning and I seem to have connected to a neighbor's headset.  That's what I get for randomly clicking stuff!  Anyway, I'm always set to "indiscoverable" and I immediately deactivated bluetooth after I realized I'd connected, but the icon for this person's device still pops up on my bluetooth menu.  Even when bluetooth is disabled.

Now, I've never actually used  a bluetooth headset before, so I'm not sure how this works.  I certainly don't want my calls being routed through this person's headset or for there to be confusion if I decide to get one of my own eventually.  Is there a way for me to remove the device from the bluetooth menu?  A  phone restart didn't seem to work, and the bluetooth menu itself doesn't let you do much more than search, activate/deactivate, or become discoverable.

Ah, that did it.  Silly me.  Superficially it seemed like the only thing tapping on the device did was enable bluetooth, and I didn't want to mess around with that.

Thanks!