  Detailed atmospheric characterization of exoplanets by transmission
spectroscopy requires careful consideration of stellar surface inhomogeneities
induced by starspots. This effect is particularly problematic for planetary
systems around M-dwarfs, and their spot properties are not fully understood. We
investigated the stellar activity of the young M-dwarf K2-25 and its effect on
transit observations of the sub-Neptune K2-25b. From multi-band monitoring
observations of stellar brightness variability using ground-based telescopes
and TESS, we found that the temperature difference between the spots and
photosphere is <190 K and the spot covering fraction is <61% (2$\sigma$). We
also investigated the effect of starspot activity using multi-epoch, multi-band
transit observations. We rule out cases with extremely low spot temperatures
and large spot covering fractions. The results suggest that spots could distort
the transmission spectrum of K2-25b by as much as $\sim$100 ppm amplitude,
corresponding to the precision of JWST/NIRSPEC of the target. Our study
demonstrates that simultaneous multi-band observations with current instruments
can constrain the spot properties of M-dwarfs with good enough precision to
support atmospheric studies of young M-dwarf planets via transmission
spectroscopy.
