I just added an icon next to the edit link. I agree it does look plain. I agree that it is too pushy, but until its got self-sustaining growth, they stay there...
It's up to you, obviously, but I found the pushiness extremely off-putting. You need to decide whether the core user activity is writing documents or inviting their friends. If it's writing documents, get rid of the invite clutter. If it's inviting friends, well, good luck, but the app is gone from my profile.