Neural transducer (RNNT)-based target-speaker speech recognition (TS-RNNT) directly transcribes a target speaker's voice from a multi-talker mixture. It is a promising approach for streaming applications because it does not incur the extra computation costs of a target speech extraction frontend, which is a critical barrier to quick response. TS-RNNT is trained end-to-end given the input speech (i.e., mixtures and enrollment speech) and reference transcriptions. The training mixtures are generally simulated by mixing single-talker signals, but conventional TS-RNNT training does not utilize single-speaker signals. This paper proposes using knowledge distillation (KD) to exploit the parallel mixture/single-talker speech data. Our proposed KD scheme uses an RNNT system pretrained with the target single-talker speech input to generate pseudo labels for the TS-RNNT training. Experimental results show that TS-RNNT systems trained with the proposed KD scheme outperform a baseline TS-RNNT.