How do I erase Eraser software itself?

Just so ...

You can't use Eraser to erase itself from the system; you can only uninstall it in the usual way. If (for some reason, and I personally cannot think of one) you want to remove all traces of Eraser, you could uninstall it, use a suitable utility such as Tweaknow to compact your Registry, then use for example CCleaner to erase the free space on your drive.

I have a company policy that forbids "unapproved software" from being installed, so it would be nice to be able to remove this application in the same fashion as it works.

Given the relatively small disk footprint of the application, wouldn't it be relatively straightforward to build a custom job that would load the application into memory and perform the deletion of the application and logs? Perhaps I'm the only person paranoid enough to want to eliminate evidence of my knowledge of the need to eliminate evidence...