vinyl floor removal for tile project

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I have hard wood base with 2 sheets of 1/4" plywood, then vinyl on top of that. Everything is 16 on center. I have removed the vinyl and the back of the vinyl still remains. My question is if I am planning on laying tile on the floor must I first remove the vinyl backing before I start or can I just tile upon it or even place backer board directly on top of it, then tile.