1. Right click Inner Space and select Configuration.
2. Click the Game Configuration tab
3. Select the Game from the first drop-down box
4. If by "profile" you meant Game, there's a "Remove Game" button. Otherwise, select the Game Profile from the next drop-down box.
5. There's a "Remove Profile" button here. Note that if you're deleting the only Game Profile(s) you might as well just click Remove Game, because now you have a Game defined with no Profiles

Couple other things to mention. If Inner Space detects a game, and you remove it (or its only profile), it's going to detect it again and list it again in the context menu next time you start IS. To avoid that, you can instead open up the Game Profile (follow steps 1-4 to get to it) and change the Path or Filename to something that doesn't exist; it will not list a game profile in the IS menu if the configured executable doesn't exist. For example, just add a letter to the executable filename.
I need to add an option to just hide any given games and profiles
