The forest was not actually cleansed at all. Several Nazgul were sent to reinhabit Dol Guldur and command growing evil within it once again, and it was a major stronghold of Sauron in the War of the Ring -- second only to Barad-dur (and perhaps Minas Morgul).
Galadriel only threw down its walls after the destruction of the Ring (and Sauron). And since the destruction of the One Ring meant the end of the time of the Three Rings, she did it without Nenya.
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"If you're referring to the incident with the dragon, I was barely involved. All I did was give your uncle a little nudge out of the door."
THE HOBBIT - IT'S COMING
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