We measure the size-mass relation and its evolution between redshifts 1<z<3, using galaxies lensed by six foreground Hubble Frontier Fields clusters. The power afforded by strong gravitation lensing allows us to observe galaxies with higher angular resolution beyond current facilities. We select a stellar mass limited sample and divide them into star-forming or quiescent classes based on their rest-frame UVJ colours from the ASTRODEEP catalogues. Source reconstruction is carried out with the recently released lenstruction software, which is built on the multipurpose gravitational lensing software lenstronomy. We derive the empirical relation between size and mass for the late-type galaxies with M_*_>3x10^9^ M_{sun}_ at 1<z<2.5 and M_*_>5x10^9^M_{sun}_ at 2.5<z<3, and at a fixed stellar mass, we find galaxy sizes evolve as R_eff_{prop.to}(1+z)^-1.05+/-0.37^. The intrinsic scatter is <0.1dex at z<1.5 but increases to ~0.3dex at higher redshift. The results are in good agreement with those obtained in blank fields. We evaluate the uncertainties associated with the choice of lens model by comparing size measurements using five different and publicly available models, finding the choice of lens model leads to a 3.7 per cent uncertainty of the median value, and ~25 per cent scatter for individual galaxies. Our work demonstrates the use of strong lensing magnification to boost resolution does not introduce significant uncertainties in this kind of work, and paves the way for wholesale applications of the sophisticated lens reconstruction technique to higher redshifts and larger samples.