Ok, this is going to be a bit lengthy.
As you have said, your website has been affected by Penguin update; I would like to know if the website had received any mail in Google Webmaster Tool regarding unnatural links? If yes, then it is a manual penalty. In that case, you need to remove all the links that look unnatural or coming with exact matched keywords. Try get as many links down with it as possible and then give Disavow link a try before sending a reconsideration request.
But if you have not received any mail, this is probably affected by Penguin Algorithm. In that case, Disavow Link is the only way to exonerate.
Now, let me come to real part of your post. Yes, you need to get all the links down from site; all of them as the links are coming with exacted match key phrase and they are do follow. Or, else just add no follow attribute against each link.