Recently, zero-shot text-to-speech (TTS) systems, capable of synthesizing any speaker's voice from a short audio prompt, have made rapid advancements. However, the quality of the generated speech significantly deteriorates when the audio prompt contains noise, and limited research has been conducted to address this issue. In this paper, we explored various strategies to enhance the quality of audio generated from noisy audio prompts within the context of flow-matching-based zero-shot TTS. Our investigation includes comprehensive training strategies: unsupervised pre-training with masked speech denoising, multi-speaker detection and DNSMOS-based data filtering on the pre-training data, and fine-tuning with random noise mixing. The results of our experiments demonstrate significant improvements in intelligibility, speaker similarity, and overall audio quality compared to the approach of applying speech enhancement to the audio prompt.