Maybe I'm clashing with the specific phrasing since I haven't heard of a bias in the grading itself (i.e. a bias of the teacher), but rather a bias of the system. Schooling as a whole aligns more with girls' strengths as they're more consistent in the day-to-day (ex: organization, planning, homework) whereas boys tend to test better [0]. The weighting of assignments in a particular class could tip the benefit in either direction.
I could believe girls 'get graded higher' on written assignments due to generally better handwriting. I had poor handwriting (though recall at least one girl classmate with worse) and certainly received no credit on some correct answers as a result. I imagine a frustrated teacher reading through a chicken-scratch essay might dock some points - whether directly with a note calling it out (also happened to me), discreetly, or subconsciously.
[0]: https://www.theatlantic.com/education/archive/2014/09/why-gi...
Getting personalized feedback (encouragement, small corrections, etc) can mean much more to a student than a simple green checkmark/red x somewhere. Good educators can know when to apply the right amount of pushing or backing off that can help a student succeed.
Ideally, of course. Lots of bad teachers out there…