MacOS – Background menu bar stuff visible through current menu bar

This happens to me too sometimes. A guaranteed solution: Restart the menu bar. Here's how:

Open Terminal (/Applications/Utilities). Type: killall SystemUIServer.
killall restarts the following process, and SystemUIServer is the process in charge of the menu bar.
Once you press enter, the menu bar will disappear and reappear. It should be working fine.

There are a few places where items can get launched, and the most common place is in System Preferences > Login > Startup Items. That's the goto place for most issues like this.

Removing the Application doesn't always remove all traces, especially if the App was installed by an installation script, rather than simply being dragged into your Applications folder in the first place. Scripted installs often perform all sorts of background installs, such as kernel extensions, and helper apps that sit in the Menu Bar, and the startup items list is the common place to fire them up.