  We present a study of the extinction and depletion-derived dust properties of
gamma-ray burst (GRB) absorbers at $1<z<3$ showing the presence of neutral
carbon (\ion{C}{I}). By modelling their parametric extinction laws, we discover
a broad range of dust models characterizing the GRB \ion{C}{I} absorption
systems. In addition to the already well-established correlation between the
amount of \ion{C}{I} and visual extinction, $A_V$, we also observe a
correlation with the total-to-selective reddening, $R_V$. All three quantities
are also found to be connected to the presence and strength of the 2175\,{\AA}
dust extinction feature. While the amount of \ion{C}{I} is found to be
correlated with the SED-derived dust properties, we do not find any evidence
for a connection with the depletion-derived dust content as measured from
[Zn/Fe] and $N$(Fe)$_{\rm dust}$. To reconcile this, we discuss a scenario
where the observed extinction is dominated by the composition of dust particles
confined in the molecular gas-phase of the ISM. We argue that since the
depletion level trace non-carbonaceous dust in the ISM, the observed extinction
in GRB \ion{C}{I} absorbers is primarily produced by carbon-rich dust in the
molecular cloud and is therefore only observable in the extinction curves and
not in the depletion patterns. This also indicates that the 2175\,{\AA} dust
extinction feature is caused by dust and molecules in the cold and molecular
gas-phase. This scenario provides a possible resolution to the discrepancy
between the depletion- and SED-derived amounts of dust in high-$z$ absorbers.
