It would be helpful if scores were saved every time a quiz was complete, but only when the score is above threshold would it disappear from the students view. Is this feature available?
When you click on a test name to configure its options, there is an option that looks like this:
Save grades when score ≥ N
When you enter some number N for a minimum score, the grades are not saved in the sense that they would appear in your grade table. However, thatquiz.org does keep a record of this attempt. You can access this discarded grade by looking at the grade report. Click on the test name on your grades page for the report. Or, check the test name in the list of tests for the class and then click the "Grades" button.
On the grade report, if any students missed the minimum score, you'll see a link that says "Discarded grades". Click the link, and you'll see all the discarded grades. You can even choose to accept a discarded grade, in which case it will become visible in your grades table and disappear from the student's view.