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We present high-resolution and multi-line observations of a C2-class solar flare, occurred in NOAA AR 12740 on May 6, 2019. The rise, peak and decay phases of the flare were recorded continuously and quasi-simultaneously in the Ca II K line with the CHROMIS instrument, the Ca II 8542 and Fe I 6173 Ålines with the CRISP instrument at the SST. The observations in the chromospheric Ca II lines exhibit intense brightening near the flare footpoints. At these locations, a non-LTE inversion code was employed to infer the temperature, magnetic field, line-of-sight (LOS) velocity and microturbulent velocity stratification in the flaring atmosphere. During the flare peak time, the LOS velocity shows both upflows and downflows around the flare footpoints in the upper chromosphere and lower chromosphere, respectively. Moreover, the temporal analysis of the LOS magnetic field at the flarepoints exhibits a maximum change of ~600 G. After the flare, the LOS magnetic field decreases to the non-flaring value, exhibiting no permanent or step-wise change. The analysis of response functions to the temperature, LOS magnetic field and velocity shows that the Ca II lines exhibit enhanced sensitivity to the deeper layers (i.e., log_t ~ -3) of the flaring atmosphere, whereas for the non-flaring atmosphere they are mainly sensitive around log_t ~ -4. We suggest that a fraction of the apparent increase in the LOS magnetic field at the flare footpoints may be due to the increase in the sensitivity of the Ca II 8542 Åline in the deeper layers, where the field strength is relatively stronger. The rest can be due to magnetic field reconfiguration during the flare. Our observations illustrate that even a less intense C-class flare can heat the deeper layers of the solar chromosphere, mainly at the flare footpoints, without affecting the photosphere.