To ignore a Penguin all you need to do is open their player card, which you can do by clicking their Penguin. Then, from there click the skull button (see picture below).
This will completely remove that Penguin from your screen so you no longer have to see or interact with them again.
If you wish to stop ignoring a Penguin, you can do so by opening your Ignore List by clicking the skull button from the Friends List menu. Then, click the Penguin you wish to stop ignoring, which will bring up their player card. From there, click the skull button with the red X over it.
