Rotate links for registered users

Hi there

I am trying to do the following:

I have a wordpress website that has a lot of adfly links in it. I want to make it so that if a user registers it removes all the adfly links and replaces them with the real links.

End result wanted:
Unregistered users see the adfly ads, registered users do not.

If there are any plugins available to do this I would love it.

I have no programming knowledge so if the answers are as simple as possible I would appreciate it!