We present K-band imaging observations of ten Gamma-Ray Burst (GRB) host galaxies. We compare their observed and absolute K magnitudes as well as their R-K colours with those of other distant sources detected in various optical, near-infrared, mid-infrared and submillimeter deep surveys. We find that the GRB host galaxies, most of them lying at 0.5<z<1.5, exhibit very blue colours, comparable to those of the faint blue star-forming sources at high redshift. They are sub-luminous in the K-band, suggesting a low stellar mass content. We do not find any GRB hosts harbouring R- and K-band properties similar to those characterizing the luminous infrared/submillimeter sources and the extremely red starbursts. Should GRBs be regarded as an unbiased probe of star-forming activity, this lack of luminous and/or reddened objects among the GRB host sample might reveal that the detection of GRB optical afterglows is likely biased toward unobscured galaxies. It would moreover support the idea that a large fraction of the optically-dark GRBs occur within dust-enshrouded regions of star formation. On the other hand, our result might also simply reflect intrinsic properties of GRB host galaxies experiencing a first episode of very massive star formation and characterized by a rather weak underlying stellar population. Finally, we compute the absolute B magnitudes for the whole sample of GRB host galaxies with known redshifts and detected at optical wavelengths. We find that the latter appear statistically even less luminous than the sub-luminous blue sources which mostly contributed to the B-band light emitted at high redshift. This indicates that the formation of GRBs could be favoured in particular systems with very low luminosities and, therefore, low metallicities. (Abridged)
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