In situ measurements of interstellar dust grains with the Cassini's Cosmic Dust Analyzer have surprisingly revealed a very low carbon abundance, in apparent contradiction with recent interstellar dust models based on many types of astronomical observations that predict a significant fraction of carbonaceous particles in addition to olivine-type & pyroxene-type silicates. It has been suggested that this is due to the lower mass and higher charge-to-mass ratio of carbonaceous grains, which favor their exclusion from the heliosphere by the solar wind. If this is the case, dust analyzers on board an interstellar probe should measure a greater carbon abundance and better constrain the relationship between grain size and composition. The detection of organic grains is of crucial importance after discoveries of the Rosetta mission of the very large fraction of organic matter of comet Churyumov-Gerasimenko and its most likely pristine nature. It could also shed light on the potential accretion on the grains of the carbonaceous macro-molecules that cause the hundreds of diffuse interstellar absorption bands that contaminate the spectra of highly reddened stars, including the bands recently identified as due to the fullerene cation C60+.