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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Low Temperature Physics 43, 383 (2017) and may be found at https://doi.org/10.1063/1.4979362 ; The kinetics of the sorption and the subsequent desorption of 4He by the starting graphite oxide (GtO) and the thermally reduced graphene oxide samples (TRGO, Treduction = 200, 300, 500, 700 and 900 °C) have been investigated in the temperature interval 1.5–20 K. The effect of the annealing temperature on the structural characteristics of the samples was examined by the x-ray diffraction (XRD) technique. On lowering the temperature from 20 to 11–12 K, the time of 4He sorption increased for all the samples, which is typically observed under the condition of thermally activated diffusion. Below 5 K the characteristic times of 4He sorption by the GtO and TRGO-200 samples were only weakly dependent on temperature, suggesting the dominance of the tunnel mechanism. In the same region (T < 5 K) the characteristic times of the TRGOs reduced at higher temperatures (300, 500, 700 and 900 °C) were growing with lowering temperature, presumably due to the defects generated in the carbon planes on removing the oxygen functional groups (oFGs). The estimates of the activation energy (Ea) of 4He diffusion show that in the TRGO-200 sample the Ea value is 2.9 times lower as compared to the parent GtO, which is accounted for by GtO exfoliation due to evaporation of the water intercalated in the interlayer space of carbon. The nonmonotonic dependences Ea(T) for the GtO samples treated above 200 °C are determined by a competition between two processes—the recovery of the graphite carbon structure, which increases the activation energy, and the generation of defects, which decreases the activation energy by opening additional surface areas and ways for sorption. The dependence of the activation energy on Treduction correlates well with the contents of the crystalline phase in GtO varying with a rise of the annealing temperature. ; Financial support from Spanish Ministry MINECO and the European Regional Development Fund (Project No. ENE2013-48816-C5-5-R), the Regional Government of Aragon and the European Social Fund DGA-ESF (Project No. T66) and Targeted Comprehensive Fundamental Research Program of NASU (Project No. 6/16-H) is gratefully acknowledged. ; Peer reviewed