iTunes still showing deleted songs - how do I stop this?

I have a 2015 MacBook Pro Retina. I booted this computer from a backup of an old MacBook. On the old computer, I had an extensive iTunes library, which I had deleted entirely before creating the backup that the newer computer (the Retina) was booted from. My iTunes library on the newer computer still the shows all songs I had on my original computer before I deleted them. Only now, there is an exclamation point next to all the songs (because the files are missing).

Basically, I want iTunes to show only the songs that are actually in it. I.e. I don't want it to list any of the old songs that were once in it but now are deleted. How do I facilitate this?