Abstract About 6% of Radio Galaxies (RG) can reach linear sizes larger than 0.7 Mpc, and are then classified as Giant Radio Galaxies (GRG). The conditions that make possible the formation of such big structures is still not clear - either core accretion properties or environmental factors. Recent studies have shown that GRG can be up to four times more abundant in hard X-ray selected (i.e. from INTEGRAL/IBIS and Swift/BAT at >20 keV) RG samples. Moreover, a high fraction of young radio sources found in their cores suggests a recently restarted activity, as suggested from the discrepancy between the measured jet and lobes power, with respect to the one expected from core X-ray luminosity. Here we present a radio morphological study of a sample of 15 hard X-ray selected GRG, discussing low-frequency images from our GMRT campaign complemented with others from the literature: among them, 7/15 show evidence of restarted radio activity either in the form of double-double/X-shaped morphology, or as a cocoon emission embedding more recent jets. This, together with the objects from this sample already found hosting a young radio source in their core, suggests that at least 13 over 15 of these hard X-ray selected GRG show features which are consistent with the possibility of restarted radio activity.