  The non-stationary relaxation and physical ageing in the diffusion-limited
erosion process ({\sc dle}) is studied through the exact solution of its
Langevin equation, in $d$ spatial dimensions. The dynamical exponent $z=1$, the
growth exponent $\beta=\max(0,(1-d)/2)$ and the ageing exponents $a=b=d-1$ and
$\lambda_C=\lambda_R=d$ are found. In $d=1$ spatial dimension, a new
representation of the meta-conformal Lie algebra, isomorphic to
$\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{sl}(2,\mathbb{R})$, acts as a
dynamical symmetry of the noise-averaged {\sc dle} Langevin equation. Its
infinitesimal generators are non-local in space. The exact form of the full
time-space dependence of the two-time response function of {\sc dle} is
reproduced for $d=1$ from this symmetry. The relationship to the
terrace-step-kink model of vicinal surfaces is discussed.
