Recently, probably by some accidental key-combination stroke during furious development, my IntelliSense window has a small text input field above which is really annoying, because I can no longer just type and hit Enter to use the autocompletion feature.
How do I get rid of it?

The key combination you probably pressed was Ctrl + Alt + Space, which toggles the completion methods of intellisense.
Can be switched back to the other completion mode by going to:
Edit-> Intellisense -> Toggle Completion Mode.