Phase recovery is an essential process for reconstructing a time-domain signal from the corresponding spectrogram when its phase is contaminated or unavailable. Recently, a phase recovery method using deep neural network (DNN) was proposed, which interested us because the inverse short-time Fourier transform (inverse STFT) was utilized within the network. This inverse STFT converts a spectrogram into its time-domain counterpart, and then the activation function, leaky rectified linear unit (ReLU), is applied. Such nonlinear operation in time domain resembles the speech enhancement method called the harmonic regeneration noise reduction (HRNR). In HRNR, a time-domain nonlinearity, typically ReLU, is applied for assistance in enhancing the higher-order harmonics. From this point of view, one question arose in our mind: Can time-domain ReLU solely assist phase recovery? Inspired by this curious connection between the recent DNN-based phase recovery method and HRNR in speech enhancement, the ReLU assisted Griffin-Lim algorithm is proposed in this paper to investigate the above question. Through an experiment of speech denoising with the oracle Wiener filter, some positive effect of the time-domain nonlinearity is confirmed in terms of the scores of the short-time objective intelligibility (STOI).