Select a stain remover to treat the stain. There are commercial stain removers you can use, but household products like rubbing alcohol also work to loosen stains.
Apply the stain remover to a clean cloth rather than on the partition itself. Depending on how your cubicle partitions are constructed, you want to avoid over-wetting.
Blot the treated cloth gently on the ink stain to help soften any dried ink. Do not rub the stain, as this spreads the ink and makes it worse.
Absorb the moisture and the wet ink with a dry, white cloth. Repeat as necessary, until the ink transfers onto the white cloth and disappears from the partition wall.
Blot the now clean area with a moistened sponge to rinse it. Allow to dry.