Modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimates of the Hubble constant. The source position transformation (SPT), which covers the well-known mass-sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. The pySPT program also comes with a subpackage dedicated to simple lens modeling. This can be used to generate lensing related quantities for a wide variety of lens models independent of any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in a previous work between a softened power law and composite (baryons + dark matter) lenses. We find that the large deviations previously predicted have been overestimated because of a minor bug in the public lens modeling code lensmodel (v1.99), which is now fixed. We conclude that the predictions for the Hubble constant deviate by ∼7%, first and foremost as a consequence of an MST. The latest version of pySPT is available on Github, a software development platform, along with some tutorials to describe in detail how making the best use of pySPT.