I guess she wanted to get to the Lancelot's room sneaky using the key she has got. And she put on the socks as she wanted to look not so ladylike. But it's still not clear for me.
Answer:
Explanation: According to the context of the previous statement, the most probable meaning of the word permeate would be "saturated"; since the meaning of the word permeate is the action of penetrating a body or passing through it. In the previous text the cotton clothing is soaked with water, this means that the water permeated and penetrated the clothes, to the point that it could saturate it with this liquid.
