Unfortunately, we don’t have the sort of filtering in our API where you can query to a subset of tasks that match an arbitrary pattern that you specify (i.e. “only completed tasks that were completed since a specified date”). We also don’t have an easy way to only get the completed tasks. You can get all incomplete tasks fairly easily by specifying
completed_since=now on the tasks query endpoint. This is admittedly a bit strange, but works, however, the converse (get only tasks completed by a specific date) doesn’t exist. Per the task query docs,
completed_since returns tasks that are either incomplete or that have been completed since this time. There is no way to return just the completed tasks.
We are evaluating adding more filitering to the API, so you might see it at some point!n For now, however, the only way to go about this is to get all the tasks and filter out the incomplete ones on your side.