Context. TMR-1 (IRAS 04361+2547) is a class I proto-stellar source located in the nearby Taurus star-forming region. Its circumstellar environment is characterized by extended dust emission with complex structures and conspicuous filaments. A faint companion, called TMR-1C, located near the proto-star was detected in previous studies, but its nature as a very young substellar object remains inconclusive. Aims. We aim to improve the constraints on the nature of the faint object TMR-1C, and to investigate the process of very low-mass star formation in the TMR-1 system. Methods. Using very sensitive infrared imaging observations of the TMR-1 system and near-infrared spectroscopy, we compile the spectral energy distribution (SED) of TMR-1C over a much wider wavelength range than possible in previous work. We then compare the spectral energy distribution with models of extincted background stars, young sub-stellar objects, and very low-mass stars with circumstellar disk and envelope emission. We also search for additional low-luminosity sources in the immediate environment of the TMR-1 proto-stellar source. Furthermore, we study the surrounding near-infrared dust morphology, and analyse the emission line spectrum of a filamentary structure in the physical context of a bow-shock model. Results. We find that the observed SED of TMR-1C can be reproduced by neither an extincted background star, nor available models for a young extremely low-mass ( 12 M J ) object. Our near-infrared spectrum allows us to infer an effective temperature 3000 K. We achieve a close fit of TMR-1C's SED using radiation transfer models of young stellar objects with circumstellar disks, hence propose that TMR-1C is most likely a very low-mass star with M ≈ 0.1−0.2 M surrounded by a circumstellar disk of high inclination, i > 80 • . Interestingly, we detect an additional very faint source, which we call TMR-1D, that is remarkably symmetrical in terms of position with TMR-1C. Both TMR-1C and TMR-1D may have formed from a common star-formation event, triggered by a powerful outflow or by the collision of primordial proto-stellar disks. The impact of an outflow is traced by molecular hydrogen emission that we detect from a distinct filament pointing towards TMR-1C. A comparison with C-type bow shock models confirms that the emission is caused by shock excitation.