How should a female teacher deal with money she earned as a result of not completing the curriculum explanation for students due to time constraints? Is this money considered unlawful, and what are the ways to dispose of it?

If the reason for not completing the courses was due to time constraints, not negligence on your part, then there is no blame upon you regarding the previous salaries. However, if it was due to your negligence, then you must seek forgiveness (Istighfar), estimate the times when you were negligent, and pay the equivalent amount from your money back to the responsible party if possible. Otherwise, give it as charity to the poor and needy or spend it on general Muslim welfare. If you do not know the exact amount, strive to estimate it and aim for the amount that you believe will clear your conscience.