In this work, we re-think the task of speech enhancement in unconstrained real-world environments. Current state-of-the-art methods use only the audio stream and are limited in their performance in a wide range of real-world noises. Recent works using lip movements as additional cues improve the quality of generated speech over "audio-only" methods. But, these methods cannot be used for several applications where the visual stream is unreliable or completely absent. We propose a new paradigm for speech enhancement by exploiting recent breakthroughs in speech-driven lip synthesis. Using one such model as a teacher network, we train a robust student network to produce accurate lip movements that mask away the noise, thus acting as a "visual noise filter". The intelligibility of the speech enhanced by our pseudo-lip approach is comparable (< 3% difference) to the case of using real lips. This implies that we can exploit the advantages of using lip movements even in the absence of a real video stream. We rigorously evaluate our model using quantitative metrics as well as human evaluations. Additional ablation studies and a demo video on our website containing qualitative comparisons and results clearly illustrate the effectiveness of our approach. We provide a demo video which clearly illustrates the effectiveness of our proposed approach on our website: \url{http://cvit.iiit.ac.in/research/projects/cvit-projects/visual-speech-enhancement-without-a-real-visual-stream}. The code and models are also released for future research: \url{https://github.com/Sindhu-Hegde/pseudo-visual-speech-denoising}.