Repro steps:

1. Think like a user/newbie.
2. Create a new project and import Blank.
3. Go into rig mode.
4. Add a trigger to any body part.
5. Add a behaviour to that same part.
6. Right-click the lego/gear icon for that body part.
7. Notice that there's a 'remove all behaviours' option in the context menu.
8. Right-click the trigger icon for the same body part.

Notice that there's no corresponding way to remove all triggers from that body part exposed in the menu.

In addition to creating a bit of an asymmetry between one part of the user experience and another, it looks as if there simply isn't a way to remove all triggers from a body part...