  (Abridged) We study the galaxy mass-size relation in CARLA spectroscopically
confirmed clusters at $1.4<z<2.8$, which span a total stellar mass
$11.3<\mathrm{log}(M^c_*/M_{\odot})<12.6$ (halo mass $13.5 \lesssim
\mathrm{log}(M^c_h/M_{\odot}) \lesssim 14.5$). Our main finding is that cluster
passive ETG at $z \gtrsim 1.5$ with ${\rm log}(M/M_{\odot})>10.5$ are
systematically $\gtrsim 0.2-0.3~{\rm dex}$ larger than field ETGs. The passive
ETG average size evolution is slower at $1<z<2$ when compared to the field.
This could be explained by differences in the formation and early evolution of
galaxies in haloes of a different mass. Strong compaction and gas dissipation
in field galaxies, followed by a sequence of mergers may have also played a
significant role in the field ETG evolution, but not in the evolution of
cluster galaxies. Our passive ETG mass-size relation shows a tendency to
flatten at $9.6<{\rm log}(M/M_{\odot})<10.5$, where the average size is
$\mathrm{log}(R_e/\mathrm{kpc}) = 0.05 \pm 0.22$. This implies that galaxies in
the low end of the mass-size relation do not evolve much from $z\sim 2$ to the
present, and that their sizes evolve in a similar way in clusters and in the
field. BCGs lie on the same mass-size relation as satellites, suggesting that
their size evolution is not different at redshift z $\gtrsim$ 2. Half of the
active ETGs ($\sim 30\%$ of the ETGs) follow the field passive galaxy mass-size
relation, and the other half follow the field active galaxy mass-size relation.
These galaxies likely went through a recent merger or neighbor galaxy
interaction, and would most probably quench at a later epoch and increase the
fraction of passive ETGs in clusters. We do not observe a large population of
compact galaxies, as is observed in the field at these redshifts, implying that
the galaxies in our clusters are not observed in an epoch close to their
compaction.
