Mac – 3/4 Icon in the status bar. What is that

It looks like the application is adding that icon. I checked the Level application on my phone (sort of a free demo for Carpenter) and it has a button with the same design in the upper right corner:

Tapping the button gives this screen:

Google still has some update notes cached where the developer listed this as a new feature in the App Store:

Added Quick Switch button on the top right corner to quickly switch between iHandy apps without getting back to home screen.

Normally, apps can't add custom icons to the status bar. According to this thread, they may just be overlaying the Quick Switch icon over the battery indicator: Customizing iPhone app taskbar

Try Bartender. This lets you hide (as well as re-arrange) menu bar items, as well as providing a secondary menu bar so that you can hide icons from the main bar but still have access to them on a keyboard shortcut or menu bar item.