According to Joseph Mallozzi, the series creator, the task the Android was given was finished by the end of the episode, which Two reveals to Six. Specifically, she asked the Android to check into Five's story by checking statis records and see if anyone messed with the pods.
TTVJ: Early in the episode Two pulled the Android aside and asked for a favour. Did that favour involve making the ship malfunction to test the crew?
JM: Again you can read into it what you will, but the most likely response to that is exactly how it turned out–the explanation being that she finds the kid and this is her opportunity to ask the Android to check the stasis records to find if anybody screwed with the stasis pods and confirm Five’s dream. It turns out she does confirm it, but before they have a talk to really discuss Five has already told Six. He confronts her on the bridge and she comes clean and says, ‘Look I asked her to look into this,’ which is essentially what she was talking about when she said, ‘I need you to do something for me and keep it quiet.’
I admit I didn't pick up on the connection, either, and Mallozzi's answer wasn't exactly definitive. So there may still be more going on that he's just not saying. But at the moment, it doesn't seem like there's any deeper meaning to that scene except Two's desire to keep Five's stolen memories a secret (which she fails to do.)