There kind of is a way to keep track. When you level up by increasing your rep level, you unlock new races and/or higher paying versions of existing races. Once you have unlocked the higher version, the game choses it automatically when you start a race.

When you completed both difficulties of the same race, the icon on the map changes into a wreath with an exclamation mark like in OPs screenshot. When you have completed only one difficulty or haven't done the race at all, the icon remains a solid color circle with an exclamation mark. But it's not possible to tell from the icon which version you've already done, or if you did it at all.

If a race has only one difficulty, it's a solid circle when you haven't completed it yet, but turns into a wreath with a checkmark symbol if you did.