The grade your DD earned is the grade she should get. I know it seems harsh that she missed it by .01, but she missed the cut off. What if the next lowest grade was off by .02, that person should miss out too? or since it was only .02, give them the nudge? Where should the line be drawn? I know where the line should be.....69.9 and 70.0. That is probably what the teacher has in the syllabus, and that's what should be the standard for the class.
As far as extra credit. I don't think it should be allowed. Especially to just one student to pass. She should have worked harder through out the quarter to get the grade she wanted. I'm sure there are other students who would have loved to have the chance to better their grade. Even A students might want a chance. I know my DD always does extra credit when offered. Her thinking is that it can only help.
Its only the quarter grade, she still has time to get her grade up before the semester is up.
I have a hard time getting my head around the whole fail at 69.9. At DD's school, anything below and 80 and you are in trouble. Next year it will be 85, and the last years will be 90.