We show that when observing the range of a chordal $\backslash SLE\kappa$ curve for $\kappa \in (4,8)$, it is not possible to recover the order in which the points have been visited. We also derive related results about conformal loop ensembles (CLE): (i) The loops in a $\backslash CLE\kappa$ for $\kappa \in (4,8)$ are not determined by the $\backslash CLE\kappa$ gasket.
(ii) The continuum percolation interfaces defined in the fractal carpets of conformal loop ensembles $\backslash CLE\kappa$ for $\kappa \in (8/3,4)$ (we defined these percolation interfaces in earlier work, where we also showed there that they are $\backslash SLE16/\kappa$ curves) are not determined by the $\backslash CLE\kappa$ carpet that they are defined in.