How do I remove duplicate connections in Power Pivot?

I was working with a client recently and was asked a question. "How do I remove duplicate connections in Power Pivot"? I know this is an issue and I specifically advise people to be careful in my training courses and also in my book. But of course once you have the problem, then knowledge on how to do it the correct way is really only helpful for "next time". Unfortunately the "fix" is quite manual as I don't believe there is an "easy" way to reconnect a loaded table to a different data source once you have it imported inside of Power Pivot.