Time-modulated arrays (TMAs) transmitting information bearing orthogonal frequency division multiplexing (OFDM) signals can achieve directional modulation. By turning its antennas on and off in a periodic fashion, the TMA can be configured to transmit the OFDM signal undistorted in the direction of a legitimate receiver and scrambled everywhere else. This capability has been proposed as means of securing the transmitted information from unauthorized users. In this paper, we investigate how secure the TMA OFDM system is, by looking at the transmitted signal from an eavesdropper's point of view. We demonstrate that the symbols observed by the eavesdropper across the OFDM subcarriers are linear combinations of the source symbols, with mixing coefficients that are unknown to the eavesdropper. We propose the use of independent component analysis (ICA) theory to obtain the mixing matrix and provide methods to resolve the column permutation and scaling ambiguities, which are inherent in the ICA problem, by leveraging the structure of the mixing matrix and assuming knowledge of the characteristics of the TMA OFDM system. In general, resolving the ambiguities and recovering the symbols requires long data. Specifically for the case of the constant modulus symbols, we propose a modified ICA approach, namely the constant-modulus ICA (CMICA), that provides a good estimate of the mixing matrix using a small number of received samples. We also propose countermeasures which the TMA could undertake in order to defend the scrambling. Simulation results are presented to demonstrate the effectiveness, efficiency and robustness of our scrambling defying and defending schemes.