  At fixed stellar mass $M_*$, the effective radius $R_{\rm e}$ of massive
satellite early-type galaxies (ETGs) in galaxy clusters is, on average, larger
at lower redshift. We study theoretically this size evolution using the
state-of-the-art cosmological simulation IllustrisTNG100: we sampled $75$
simulated satellite ETGs at redshift $z=0$ with $M_* \ge 10^{10.4} M_{\odot}$
belonging to the two most massive ($\approx 10^{14.6} M_{\odot} $) haloes of
the simulation. We traced back in time the two clusters' main progenitors and
we selected their satellite ETGs at $z>0$ with the same criterion adopted at
$z=0$. The $R_{\rm e}-M_*$ relation of the simulated cluster satellite ETGs,
which is robustly measured out to $z=0.85$, evolves similarly to the observed
relation over the redshift range $0\lesssim z \lesssim 0.85$. In the simulation
the main drivers of this evolution are the acquisition of new galaxies
("newcomers") by the clusters and the transformation of member galaxies located
at large clustercentric distance ("suburbanites") at $z=0.85$, which end up
being massive satellite ETGs at $z=0$. Though several physical processes
contribute to change the population of satellite ETGs in the considered
redshift interval, the shape of the stellar mass function of the simulated
cluster ETGs is not significantly different at $z=0.85$ and at $z=0$,
consistent with observations.
