I use Avast Free, so can't speak from personal experience.
From memory of this in the forums, I think this is shown for about a month and disappears automatically (presumably after that time frame it isn't likely to be reinstalled).
However, if you open your Avast Account (via the Avast UI Registration information > Go to Account), you should see the two entries (presumably where you saw them). I believe you should be able to assign the license to the system you now have and delete the entry for the other.