Haven't we seen them toggle on a Moogle icon in a hidden status icon column during the "Irregular Tomestones" moogle events? So it seems like there's already a column for status icons in there; I imagine a 'you still have a reward available' icon would be a reasonably easy add as a result.

(What'd be a little more effort but really nice would be a 'rewards' tab that shows all the duties you haven't yet gotten an award for; all the roulettes you haven't done for the day, any current raid tier stuff you haven't done for the week, etc. Make it easier to check "Did I do that thing this week yet or not?" without having to go to the specific duty's appropriate Duty Finder tab to check.)