The catalogue in FITS format from this paper: http://adsabs.harvard.edu/abs/2017arXiv170306635H This Rescaled Subset of the Alternative Data Release 1 to the Tata Institute of Fundamental Physics Giant Metrewave Radio Telescope Sky Survey (TGSS-RSADR1) modifies the initial data release of TGSS-ADR1 (Intema et al. 2017) to bring that catalogue to the same flux scale as the extragalactic catalogue from the GaLactic and Extragalactic All-sky Murchison Widefield Array survey (GLEAM: Wayth et al. 2015; Hurley-Walker et al. 2017). In this paper we motivate the derivation of correct and complementary flux density scales, introduce a methodology for correction based on radial basis functions, apply it to TGSS-ADR1, and create a modified catalogue, TGSS-RSADR1. This catalogue comprises 383,589 TGSS-ADR1 sources with updated flux density and flux density uncertainty values, and covers $\mathrm{Declination}\leq+30^\circ$, $|b|\geq10^\circ$, a sky area of 18,800 deg$^2$.