In this paper, we report a study on the use of a linear triblock copolymer based on styrene and ethylene/butylene (SEBS) and a polypropylene (PP)-based olefin block copolymer (OBC) for improving the impact strength of a recycled polypropylene (PP) from packaging waste. Talc was used as a reinforcing filler in order to prepare a material suitable for being used in the automotive sector. The composite mixtures were prepared by melt extrusion, and the samples were manufactured by injection molding. Impact strength was evaluated by Izod tests, and a morphological study of the produced fractures was performed. As a result, a composite with substantially improved impact properties was prepared, with a two-fold increase of the impact strength in the case of unnotched specimens, while only a limited positive effect was produced on notched specimens. Since talc-filled PP is a typical material used in the automotive sector, the obtained results demonstrate that post-consumer PP coming from the municipal waste collection of plastic packaging can be successfully used in car components with no compromise in terms of mechanical requirements.