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We study the striking case of a blue narrow stream with a possible globular cluster-like progenitor around the Milky Way-size galaxy NGC 7241 and its foreground dwarf companion. We present a follow-up spectroscopic study of this stream based on data taken with the MEGARA instrument at the 10.4-m Gran Telescopio Canarias using the integral field spectroscopy mode. Although our data suggest that this compact object in the stream is actually a foreground Milky Way halo star, we detect emission lines overlapping a less compact, bluer and fainter blob of the stream that is clearly visible in both ultra-violet and optical deep images. From its heliocentric systemic radial velocity derived from the [OIII] 5007A lines (V_syst= 1548.58+/-1.80 km\s^-1) and new UV and optical broad-band photometry, we conclude that this over-density 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, we calculate that the progenitor mass is between 6.4 x 10^6 Mo -2.7 x 10^7 Mo, which is typical of a dwarf galaxy. These estimates suggest that this is one of the lowest mass streams detected so far beyond the Local Group. 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. Thus, it is likely that the stream's progenitor is suffering a star-formation burst comparable to those that have shaped the star-formation history of several Local Group dwarfs in the last few Gigayears., 13 pages, 5 figures, submitted to MNRAS