Smack me down if I am off base, however because Landau-Lifshitz pseudotensor behaves as a tensor only with respect to restricted coordinate transformations, It would be considered as a part of the jet bundle within the manifold when used to this end only?

Again, let me know if I am off base, and I will delete my answer.

Because the Landau-Lifshitz pseudotensor behaves as a tensor only with respect to restricted coordinate transformations, it would be considered as a part of the jet bundle within the manifold when used to this end only.