You're looking at the list of apps for which you've created archives. You can remove an app from the list by removing all of its archives. Click on an app to see its archives. For each archive, you have two choices:
Click the archive, then press your delete key to delete the archive.
Right-click the archive, choose “Show in Finder”, and drag it to a different location, outside of Xcode's Archives folder.
Once you've deleted or moved all the archives, Xcode will remove the app from the list on the left.
If you have any difficulty to get the Library folder all you need to do is hit Command+Shift+G from the Mac desktop and type in ~/Library to temporarily access the Library directory in the Finder.
The apps will sync with all your connected accounts, so if you remove them in archives they will be returning soon (see the activity circle in the left bottom corner of organizer when you open it again). You need to leave the team that is connected to these apps. This you can do by logging in to your or your client's developers site online and choose the team in the list that will show in the right top corner under the account you have logged into. Select the regarding team that is connected to the apps you want to remove and go to membership in the bottom you will see button that says "Leave Team" (it is in red). If you them remove the apps from the archives they will not return. You or your client needs to re-invite you to the team in order to return to an active state regarding this account you left.
There is no solution for this. The list in question is populated from your iTunesConnect account so, unless Apple allows us to delete spurious items from iTunesConnect all solutions on this page will be useless because the deleted files will come back as soon as you open the Organizer panel again.
Come one Apple!
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2 years after I answered this, I must update it to say that Apple will delete these spurious apps for you if you contact them directly using one of your technical incidents. It will take weeks and it is done by exception, on request and is not guaranteed they will delete. You have to cry and explain why you want that deleted.