Double entries for Mac on iPhone continuity setting pages

I have an iPhone 6s running iOS 9.0.2 and a MacBook Pro Retina from Mid 2014 running OS X 10.11. When I go to the Settings Menu on the iPhone and go to Phone -> Calls on Other Devices, I see my MacBook two times at "Allow Calls On". Same in Messages -> Text Messages Forwarding.

Everything began after I had to reset my Mac after trying the Beta of OS X (10.11.1). I thought that it would be a good idea to configure my mac as a new Mac but it didn't take long time to make me wanna use my Time Machine backup instead of making a complete new setup of my system. But I forgot to logout from my iCloud account before deleting the new installation of OS X. So I recovered my Mac by using the Time Machine backup with OS X 10.11 and afterwards I found the double entries on my iPhone. After 40 minutes chat with the Apple support and another 60 minutes calling with the apple support, the problem still existed. Until the I had deleted my iPhone for three times. The first time, I went back to an iCloud backup from before the new installation process of the Mac - problem not solved. Then I set my iPhone up as a new iPhone without using any backup which didn't solve the problem as well. Finally I went again back to the state I had backed up before doing sth to solve the problem, because nothing seemed to fix it. On my mac I locked out from my iCloud account several times but this didn't fix the problem.

I think, because I set up my mac as a new mac with logging into my iCloud account, a new "instance" of the mac was created. Then I overwrote the hard disk before I logged out the new "instance" of the mac from iCloud which makes it impossible to log it out anymore. This "instance" was registered somewhere in iCloud which makes it appear in the continuity menus of my iPhone, even if it doesn't exist anymore.

So, for the sake of completeness, here is my question: how can i get rid of the double entry of my mac in the continuity menus of my iPhone?

Thanks

Martin