Just to be clear, I don't think there's anything wrong with giving extra credit assignments, if the teacher chooses. But the availability of extra credit should be clear to everyone, not given out because a specific student (or parent) demanded it.

Oh, absolutely: it's part of my sylabus, everyone is aware. Perhaps a bit paradoxically, it makes giving final grades much easier. If a student gets a bad grade, it's because they ignored all opportunities for improvement and I fail them with some sadness, but no regret.