its because they aren't talking about what the majority mean when they use the word "tensor". try looking into "psuedotensor". that is the established word for

its because they aren't talking about what the majority mean when they use the word "tensor". try looking into "psuedotensor". that is the established word for this for nearly a century. you may have better luck... although probably not because the main use of those historically has been in combination with tensors and tensor fields in the geometric setting and physics.