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Using a selection of Global Navigation Satellite System vertical velocities from the latest solution of the International Terrestrial Reference Frame (ITRF) ITRF2014, we calculate the degree-1 and degree-2 spherical harmonics coefficients (SHC) of the solid Earth figure changes at different dates, with realistic errors that take into account the inhomogeneity of the network. We find that the SHC are globally close to zero except the zonal coefficients, which show values notably larger than those derived from different glacial isostatic adjustment (GIA) models and which have tended to increase during the time span of observations. We show that these differences are most probably due to global recent ice melting (RIM). Assuming elastic RIM deformation, we then investigate the Earth's geocenter velocity and the geoid oblateness time evolution (J2-rate) derived from our SHC estimations. The obtained geocenter velocity reaches 0.9 ± 0.5 mm/year in 2013 with a z-component of 0.8 ± 0.4 mm/year, which is slightly larger than previous estimations. We compare our J2-rate estimations with observations. Our estimations show a similar acceleration in J2 after 2000. However, our estimates are notably larger than the observations. This indicates either that the J2-rate due to GIA processes is lower than expected (as proposed by Nakada et al., 2015, 2016) or that the deformation induced by RIM is not purely elastic, or both. Finally, we show that viscous relaxation or phase transitions in the mantle transition zone may only partly explain this discrepancy. This raises the question of the accuracy of current mass estimations of RIM and GIA models. [ABSTRACT FROM AUTHOR]