Time-modulated arrays (TMA) transmitting orthogonal frequency division multiplexing (OFDM) waveforms achieve physical layer security by allowing the signal to reach the legitimate destination undistorted, while making the signal appear scrambled in all other directions. In this paper, we examine how secure the TMA OFDM system is, and show that it is possible for the eavesdropper to defy the scrambling. In particular, we show that, based on the scrambled signal, the eavesdropper can formulate a blind source separation problem and recover data symbols and TMA parameters via independent component analysis (ICA) techniques. We show how the scaling and permutation ambiguities arising in ICA can be resolved by exploiting the Toeplitz structure of the corresponding mixing matrix, and knowledge of data constellation, OFDM specifics, and the rules for choosing TMA parameters. We also introduce a novel TMA implementation to defend the scrambling against the eavesdropper.