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.
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