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We present a study of the extinction and depletion-derived dust properties ofgamma-ray burst (GRB) absorbers at $1<z<3$ showing the presence of neutralcarbon (\ion{C}{I}). By modelling their parametric extinction laws, we discovera broad range of dust models characterizing the GRB \ion{C}{I} absorptionsystems. In addition to the already well-established correlation between theamount of \ion{C}{I} and visual extinction, $A_V$, we also observe acorrelation with the total-to-selective reddening, $R_V$. All three quantitiesare 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 becorrelated with the SED-derived dust properties, we do not find any evidencefor a connection with the depletion-derived dust content as measured from[Zn/Fe] and $N$(Fe)$_{\rm dust}$. To reconcile this, we discuss a scenariowhere the observed extinction is dominated by the composition of dust particlesconfined in the molecular gas-phase of the ISM. We argue that since thedepletion level trace non-carbonaceous dust in the ISM, the observed extinctionin GRB \ion{C}{I} absorbers is primarily produced by carbon-rich dust in themolecular cloud and is therefore only observable in the extinction curves andnot in the depletion patterns. This also indicates that the 2175\,{\AA} dustextinction feature is caused by dust and molecules in the cold and moleculargas-phase. This scenario provides a possible resolution to the discrepancybetween the depletion- and SED-derived amounts of dust in high-$z$ absorbers.

On the dust properties of high redshift molecular clouds and the connection to the 2175 {\AA} extinction bump