Griselda Marchbanks was an elderly witch who was head of the Wizarding Examinations Authority (OP31) and an elder of the Wizengamot, although (together with Tiberius Ogden) she resigned the latter office in protest at the appointment of Umbridge as ‘Hogwarts High Inquisitor’. The Daily Prophet included her in its smear campaign, insinuating that she had ‘links to subversive goblin groups’ (OP15). If the accuracy of this information is on a par with the exaggerated and inflammatory items published about Harry and Dumbledore, there may be only a few grains of truth in it; Marchbanks may have an interest in goblin rights or simply have goblin friends.
Madam Marchbanks in June 1996 was tiny and stooped, her face so lined it appeared draped in cobwebs. She is at least a decade Dumbledore’s senior, since when he was about 17, she was already working for the Wizarding Examinations Authority and personally administered his N.E.W.T.s. According to Neville, Madam Marchbanks is a bit like her friend Augusta Longbottom (OP31), implying that she is very formidable indeed, as well as stark upright. Neville also considered it unlikely that she was friendly with the Malfoys, because she’s never mentioned them, despite Draco’s claims to the contrary (OP31).
Madam Marchbanks personally examined Draco Malfoy’s practical Charms O.W.L. as well as Harry’s practical Astronomy, Divination, and Potions O.W.L.s (OP31).
When J.K. Rowling published the W.O.M.B.A.T. (Wizards’ Ordinary Magic and Basic Aptitude test) on her website in April 0f 2006, she gave Marchbanks’ name and titles as “Professor Griselda Marchbanks, CDMG, APMO, fdBB” (JKR). The meaning of the initials following her name is unclear; however, they are usually indictors of special recognition, education, or professional license.
Ahead of O.W.L.s, Draco Malfoy claims that Marchbanks is friends with his father and has had dinner at Malfoy Manor. However, Neville Longbottom doubts that this is true because he is acquainted with Marchbanks through his grandmother and has never heard her speak of Draco's family (OP31).
Other canon notes and references
Since the members of the Wizarding Examinations Authority are described as old (OP31), it's probable that Griselda Marchbanks is considerably older than Albus Dumbledore, having been born in the early or mid-1800s.
Griselda is a figure from folklore, notable for her patience (which any examiner must have).