How to take my iphone account off of itunes?

I restored my iphone 5, on my cousins computer and I did it on iTunes. Now i'm trying to do the same with my cousins phone. How can I take my phone out of iTunes and put his in. This is in his computer and I don't want my info in his computer.
And everytime I plug his ipone 5 in it says "ELIJAHS PHONE" (tHat is me) and I almost restored his phone as mine.
So basically I backed up my phone on his computer and now its stuck

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