The application range of flexible polyurethane (PU) foams is comprehensive because of their versatility and flexibility in adjusting structure and performance. In addition to the investigations associated with further broadening of their potential properties, researchers are looking for new raw materials, beneficially originated from renewable resources or recycling. A great example of such a material is ground tire rubber (GTR)—the product of the material recycling of post-consumer car tires. To fully exploit the benefits of this material, it should be modified to enhance the interfacial interactions between PU and GTR. In the presented work, GTR particles were thermo-mechanically modified with the addition of fresh and waste rapeseed oil in the reactive extrusion process. The introduction of modified GTR particles into a flexible PU matrix caused a beneficial 17–28% decrease in average cell diameters. Such an effect caused an even 5% drop in thermal conductivity coefficient values, enhancing thermal insulation performance. The application of waste oil resulted in the superior mechanical performance of composites compared to the fresh one and thermo-mechanical modification without oils. The compressive and tensile performance of composites filled with waste oil-modified GTR was almost the same as for the unfilled foam. Moreover, the introduction of ground tire rubber particles enhanced the thermal stability of neat polyurethane foam.