I have found a way to get that etch you rubbed off or you got that way. Make sure the lamp is cold when you do this. Simply breath on the lamp so it fog up. The fog first disappears on the white area. The parts where the etch used to be hang on in for a half a second before it's gone.

Problem is that you have to find the general location of the etch first. (BT shaped lamps are easy. The etch is on top.)

That works great most of the time. I have found on a couple lamps though that does not work well.

Good info to know! I use a LED flashlight and hold it at different angles until I can see the etch good but I will try what you seed FGS!