Dual-function radar-communication (DFRC) systems offer high spectral, hardware and power efficiency, as such are prime candidates for 6G wireless systems. DFRC systems use the same waveform for simultaneously probing the surroundings and communicating with other equipment. By exposing the communication information to potential targets, DFRC systems are vulnerable to eavesdropping. In this work, we propose to mitigate the problem by leveraging directional modulation (DM) enabled by a time-modulated array (TMA) that transmits OFDM waveforms. DM can scramble the signal in all directions except the directions of the legitimate user. However, the signal reflected by the targets is also scrambled, thus complicating the extraction of target parameters. We propose a novel, low-complexity target estimation method that estimates the target parameters based on the scrambled received symbols. We also propose a novel method to refine the obtained target estimates at the cost of increased complexity. With the proposed refinement algorithm, the proposed DFRC system can securely communicate with users while having high-precision sensing functionality.