Although direct deposition of polymeric materials onto textiles through 3D printing is a great technique used more and more to develop smart textiles, one of the main challenges is to demonstrate equal or better mechanical resistance, durability and comfort than those of the textile substrates before deposition process. This article focuses on studying the impact of the textile properties and printing platform temperature on the tensile and deformations of non-conductive and conductive poly lactic acid (PLA) filaments deposited onto polyethylene terephthalate (PET) textiles through 3D printing process and optimizing them using theoretical and statistical models. The results demonstrate that the deposition process affects the tensile properties of the printed textile in comparison with the ones of the textiles. The stress and strain at rupture of the first 3D printed PLA layer deposited onto PET textile material reveal to be a combination of those of the printed layer and the PET fabric due to the lower flexibility and diffusion of the polymeric printed track through the textile fabric leading to a weak adhesion at the polymer/textile interface. Besides, printing platform temperature and textile properties influence the tensile and deformation properties of the 3D printed PLA on PET textile significantly. Both, the washing process and the incorporation of conductive fillers into the PLA do not affect the tensile properties of the extruded polymeric materials. The elastic, total and permanent deformations of the 3D-printed PLA on PET fabrics are lower than the ones of the fabric before polymer deposition which demonstrates a better dimensional stability, higher stiffness and lower flexibility of these materials.