Hearing impairment (HI) disrupts social interaction by hindering the ability to follow conversations in noisy environments. While hearing aids (HAs) with noise reduction (NR) partially address this, the "cocktail-party problem" persists, where individuals struggle to attend to specific voices amidst background noise. This study investigated how NR and an advanced signal processing method for compensating for nonlinearities in Electroencephalography (EEG) signals can improve neural speech processing in HI listeners. Participants wore HAs with NR, either activated or deactivated, while focusing on target speech amidst competing masker speech and background noise. Analysis focused on temporal response functions to assess neural tracking of relevant target and masker speech. Results revealed enhanced neural responses (N1 and P2) to target speech, particularly in frontal and central scalp regions, when NR was activated. Additionally, a novel method compensated for nonlinearities in EEG data, leading to improved signal-to-noise ratio (SNR) and potentially revealing more precise neural tracking of relevant speech. This effect was most prominent in the left-frontal scalp region. Importantly, NR activation significantly improved the effectiveness of this method, leading to stronger responses and reduced variance in EEG data and potentially revealing more precise neural tracking of relevant speech. This study provides valuable insights into the neural mechanisms under- lying NR benefits and introduces a promising EEG analysis approach sensitive to NR effects, paving the way for potential improvements in HAs.