An important thing to clear up here is that Khobragade was not a full "diplomat" at the time of her arrest but rather a "consular official" who receives a limited type of immunity that only applies to laws broken while carrying out official duties.
Also the most serious charge against her isn't the wage dispute but perjury resulting from incorrect data she put on the visa forms.
India has subsequently promoted her from the NY consulate to the Indian diplomatic mission to the UN and has claimed retroactive diplomatic immunity for her, but there are procedural questions about this move.