Your belief needs to go back to chemistry class.
TSP stands for Tri-Sodium-Phosphate. There is no chlorine in it.
You’re right. My mistake comes from comparing Oxi-Clean versus Oxyclean, not TSP. Oxyclean is a chlorinated cleaner and is not the one I’m recommending. Both TSP and Oxi-Clean have no chlorine. I haven’t taken chemistry classes in decades. The old mind is rusty.
And there are, now, NO phosphates in TSP...