We use dust scaling relations to investigate the hypothesis that Virgo cluster transition-type dwarfs are infalling star-forming field galaxies, which is argued based on their optical features (e. g. discs, spiral arms and bars) and kinematic properties similar to late-type galaxies. After their infall, environmental effects gradually transform them into early-type galaxies through the removal of their interstellar medium and quenching of all star formation activity. In this paper, we aim to verify whether this hypothesis holds using far-infrared diagnostics based on Herschel observations of the Virgo cluster taken as part of the Herschel Virgo Cluster Survey. We select transition-type objects in the nearest cluster, Virgo, based on spectral diagnostics indicative for their residual or ongoing star formation. We detect dust (M-d similar to 10(5-6) M-circle dot) in 36 per cent of the transition-type dwarfs located on the high end of the stellar mass distribution. This suggests that the dust reservoirs present in non-detections fall just below the Herschel detection limit (less than or similar to 1.1 x 10(5) M-circle dot). Dust scaling relations support the hypothesis of a transformation between infalling late-type galaxies to quiescent low-mass spheroids governed by environmental effects, with dust-to-stellar mass fractions for transition-type dwarfs in between values characteristic for late-type objects and the lower dust fractions observed in early-type galaxies. Several transition-type dwarfs demonstrate blue central cores, hinting at the radially outside-in removal of gas and quenching of star formation activity. The fact that dust is also confined to the inner regions suggests that metals are stripped in the outer regions along with the gas. In the scenario of most dust being stripped from the galaxy along with the gas, we argue that the ejected metals by transition-type dwarfs significantly contribute to the enrichment of the intracluster medium over the lifetime of the Virgo cluster. The accretion of gas through tidal interactions and re-ignition of star formation in the centres of transition-type dwarfs could provide an alternative explanation for the observed dust scaling relations and blue central cores.