> False positive matches are possible, but false negatives are not – in other words, a query returns either "possibly in set" or "definitely not in set". Elements can be added to the set, but not removed (though this can be addressed with a "counting" filter); the more elements that are added to the set, the larger the probability of false positives.
So I don't think they're the right choice for this problem, if you actually depend on the result "not here" vs "never was here" being right.
The only info that needs to be stored is the ID of the finished task. If, say, the ID is expressed as a GUID then we're talking about 4 ints or 2 longs worth of data.
Even so, these records are supposed to be garbage collected.
Also deleting is far from free of side effects.