Laser-initiated switching of magnetization direction in ferrimagnetic rare-earth-transition-metal (RE-TM) alloys - whether laser induced or photothermal via compensation point - is being vigorously pursued owing to the promise of extending operating frequencies of magnetic devices into the terahertz regime. Despite intense interest, however, the effects of repeated laser exposure on the film structure and subsequent switching behavior have yet to be investigated. In order to better understand the correlated effects of femtosecond-laser irradiation on both the magnetic response and photoinduced morphological variations of RE-TM alloys, we performed in situ Fresnel transmission electron microscopy (TEM) on Tb23Co77 thin films with Ta protecting layers. Via optical access to the specimen in a modified TEM, we irradiated the thin films in situ with both individual and series of femtosecond optical pulses, and correlated laser-induced changes in magnetic domain-wall formation and growth with photothermal crystal formation and accompanying pinned magnetic sites. We find that, for a range of applied laser fluences and numbers of individual pulses, several distinct regions are formed displaying varied magnetic behavior (switchable, nonswitchable, demagnetized) and morphological features (small-to-large crystal-grain variations). Through a series of systematic studies, we quantified these linked magnetic and morphological properties as a function of laser fluence, number of pulse-train cycles, and number of individual femtosecond-laser pulses and the duration between each. Our results show how the sensitive connection between magnetic behavior and morphological structure can emerge in magneto-optic experiments across several parameters, thus illustrating the need for rigorous characterization so that potential operating regimes may be universally identified.