Ah ok. I feel as though they would continue with their protest even if there was a fine incurred, but if they were threatened with something that could impact the eventual winner of the championship, then maybe that might make them reconsider their protest?Nope. FIA don't want the bad press that would come with that.
Getting an additional yellow card for perhaps England's most important player might have a direct impact in a knock-out game down the road – so I can see why that threat is one that they have taken more seriously than a meaningless fine.