This can refer either to the grade a grad student TA gives to a student, or to a grade the grad student receives from her seminar professor. Both definitions also have several meanings. A "grade" in the student-TA relationship is a fraught thing, for while the student sees it as something he or she (or the parents) paid good monies for (i.e. it should be an "A"), the TA views it as an objective assessment of a student's work (in 99% of cases, the student's expectation and the TA's assessment do not agree). A "grade" in the grad-student--seminar-professor relationship is also a fraught thing, for the grad student is lucky to get the seminar paper back at all. If said grad student does receive the paper, the grade will usually be an empty "A" or "B," preceded by a whole string of sometimes harsh critical commentary.
Sample sentence: "This is the wrong grade, instructor. You should have given me an A."