Well, with respect to recovery by itself, I dont think running will hurt your training recovery.
I think the question you should be asking, or the thing you should be concerned about is, am I going to make optimal progress in either area when I am do things of opposite disciplines?
Running, especially long distance running requires an adaptation of your body. That adaptation is to make your muscles more efficient and use less energy each time you run that specific distance. If you run 4 miles today, you are going to expend X amount of energy. If you continue to run that 4 miles again and again, your body is going to adapt to make sure you use less and less energy to accomplish that 4 mile run. (That is why running is not an ideal long term fat loss tool). So, what does your body do to make you more efficient? It makes muscles smaller, smaller muscles use less energy. Plain and simple.
If you are doing TBT, or any type of weight training, your goal is most likely to get stronger and/or get bigger muscles. Weight training requires an adaptation of your body as well. That adaptation is to make your muscles larger to accomplish the task of moving a heavy weight. Plain and simple.
So, with that said, I would make the argument that you are not hindering your recovery so much as you are hindering your potential progress in either direction. If you want to become more muscular, which is the more difficult and time sensitive body adaptation, you might want to consider scrapping the running, as it will require the body to counteradapt. If you are concerned about being ‘Fit’, as if a level of cardiovascular fitness cant be achieved through weight training, then there are much more beneficial accessory cardio things that can be done that wont interfere with the weight training adaptation. I.E. jumping rope(great cardio/fitness tool)
