In this work we study the striking case of a narrow blue stream with a possible globular cluster-like progenitor around the NGC 7241 galaxy and its foreground dwarf companion. We want to figure out if the stream was generated by tidal interaction with NGC 7241 or if it first interacted with the foreground dwarf companion and later both fell together toward NGC 7241. We used four sets of observations, including a follow-up spectroscopic study of this stream based on data taken with the MEGARA instrument at the 10.4m Gran Telescopio Canarias using the integral field spectroscopy mode, the Mount Lemmon 0.80m telescope, the Telescopio Nazionale Galileo, the DESI Imaging Legacy surveys, and GALEX archival data. We also used high-resolution zoomed-in cosmological simulations. Our data suggest that the compact object we detected in the stream is a foreground Milky Way halo star. Near this compact object we detect emission lines overlapping a less compact, bluer, and fainter blob of the stream that is clearly visible in both ultraviolet and optical deep images. From its heliocentric systemic radial velocity derived from the [OIII]{lambda}5000{AA} lines (Vsyst=1548.58+/-1.80km/s) and new UV and optical broadband photometry, we conclude that this overdensity could be the actual core of the stream, with an absolute magnitude of Mg~-10 and a g-r=0.08+/-0.11, consistent with a remnant of a low-mass dwarf satellite undergoing a current episode of star formation. From the width of the stream and assuming a circular orbit, we calculate that the progenitor mass can be typical of a dwarf galaxy, but it could also be substantially lower if the stream is on a very radial orbit or if it was created by tidal interaction with the companion dwarf instead of with NGC 7241. These estimates also suggest that this is one of the lowest mass streams detected to date beyond the Local Group. Finally, we find that blue stellar streams containing star formation regions are commonly predicted by high-resolution cosmological simulations of galaxies lighter than the Milky Way. This scenario is consistent with the processes explaining the bursty star formation history of some dwarf satellites, which are followed by a gas depletion and a fast quenching once they enter within the virial radius of their host galaxies for the first time. Thus, it is likely that the stream's progenitor is undergoing a star formation burst comparable to those that have shaped the star formation history of several Local Group dwarfs in the last few gigayears.