EDIT: I've found my error: The Value Type in the screenshot has to be set to "Value" and not to "Game Variable" like I thought intuitively.
Pretty sure I'm missing something obvious, here (yes, I did)... I've set up a Game Variable float "Reputation" and set it to 500 at the start. I've made a button that displays the current Reputation and also adds 100 to it when clicked, no problem.
I set my BattleComponent like this:
To me it looks like it should work but Reputation doesn't change at all. I've tried checking and unchecking various checkboxes, including "Use Scene ID" hoping that destroying the Battle Component would trigger the "Set After Battle" part, but to no avail. I've also tried to set Game Variable Conditions in case there has to be one, but that doesn't help (or work?), either.
Maybe it has something to do with the fact that the battle is started in code with
Any other changes to battleComponent1 in the editor do apply to the battle, though.