Long-lived radon daughters are a critical background source in experiments searching for low-energy rare events. Originating from radon in ambient air, radioactive polonium, bismuth and lead isotopes plate-out on materials that are later employed in the experiment. In this paper, we examine cleaning procedures for their capability to remove radon daughters from PTFE surfaces, a material often used in liquid xenon TPCs. We find a large difference between the removal efficiency obtained for the decay chains of 222 Rn and 220 Rn. This indicates that the plate-out mechanism has an effect on the cleaning success. While the long-lived 222 Rn daughters can be reduced by a factor of  2, the removal of 220 Rn daughters is up to 10 times more efficient depending on the treatment. Furthermore, the impact of a nitric acid based PTFE cleaning on the liquid xenon purity is investigated in a small-scale liquid xenon TPC.