Is it permissible for a female student to seek mediation (a recommendation) from a close professor to ensure her exam papers are graded and her scores reviewed accurately, due to professors typically not grading exam papers and the prevalence of injustice in scores?

If the recommendation means scrutinizing the student's papers to grant her the grades she deserves without injustice, then this is permissible, in fact, it is recommended, because removing injustice is a شرعي [religiously mandated] requirement. However, if the recommendation means giving the student higher grades than she deserves, then this is blatant deception and injustice.