Click on the indicator for your network, or go to Network under System settings.
Then, click on Mobile Broadband and select the network that you do not want to keep any longer. Then, click on the Delete button to the right.
Here is a screenshot of where that button is. This is me demonstrating from my Wireless network selection, but it applies for Mobile Broadband too. I don't have any Mobile Broadband connections, so I demonstrated with my Wireless selection.
I hope this helps!
If the steps above do not work, try the following:
Open up terminal and run the following commands:
(Copy down the connection names that you want to keep)
sudo mkdir /etc/NetworkManager/system-connections1
sudo cp (CONNECTION 1 NAME YOU WANT TO KEEP) /etc/NetworkManager/system-connections1
sudo cp (CONNECTION 2 NAME YOU WANT TO KEEP) /etc/NetworkManager/system-connections1
(Repeat for every one you would like to keep)
sudo rm -r /etc/NetworkManager/system-connections
sudo mv /etc/NetworkManager/system-connections1 /etc/NetworkManager/system-connections
Now, it SHOULD be correct. If not, let me know in the comments.
So you understand what the commands did ran are to do, you are creating a temporary folder for the connections you want to keep, moving them to that temporary folder, deleting the entire folder with the other names so you don't need to delete every individual one, and moving the temporary folder to the place of the old one, so your system thinks that's the original folder. Unity --replace will simply redraw your desktop to refresh the list to what you need.