We can say that John is ultimately responsible for Linda’s death by the very fact of his existence.  When Linda got lost on the reservation, she was pregnant.  Getting pregnant and actually having a child is something that is very shameful in their society, really to the point of being unthinkable and unspeakable.  If Linda had found that she was pregnant while in the World State, she could simply have had an abortion and all would have been well.  But she was not in the World State and ended up having John.  Because she had him, she felt she could not go back to civilization in her youth.  As she tells John in Chapter 8,

Having young ones like an animal … If it hadn't been for you, I might have gone to the Inspector, I might have got away. But not with a baby. That would have been too shameful.

Having John trapped Linda on the reservation.  While she was trapped there, her life changed.  She essentially lived by selling her body to men.  Then she got fat and lost teeth and generally became physically unattractive.  When she finally returned to the World State, the shock of being back in civilization was too much for her since she was a freak to the people there.  She was old-looking, fat, and worst of all a mother.

Thus, having John essentially doomed Linda and he can be said to have caused her death.