Aims. We determine the starspot detection rate in exoplanetary transit light curves for M and K dwarf stars observed by the Transiting Exoplanet Survey Satellite (TESS) using various starspot filling factors and starspot distributions.Methods. We used 3.6 x 10(9) simulations of planetary transits around spotted stars using the transit-starspot model PRISM. The simulations cover a range of starspot filling factors using one of three distributions: uniform, polar-biased, and mid-latitude. After construction of the stellar disc and starspots, we checked the transit cord for starspots and examined the change in flux of each starspot to determine whether or not a starspot anomaly would be detected. The results were then compared to predicted planetary detections for TESS.Results. The results show that for the case of a uniform starspot distribution, 64 9 M dwarf and 23 +/- 4 K dwarf transit light curves observed by TESS will contain a starspot anomaly. This reduces to 37 +/- 6 M dwarf and 12 +/- 2 K dwarf light curves for a polar-biased distribution and 47 +/- 7 M dwarf and 21 +/- 4 K dwarf light curves for a mid-latitude distribution.Conclusions. Currently there are only 17 M dwarf and 10 K dwarf confirmed planetary systems from TESS, none of which are confirmed as showing starspot anomalies. All three starspot distributions can explain the current trend. However, with such a small sample, a firm conclusion cannot be made at present. In the coming years when more TESS M and K dwarf exoplanetary systems have been detected and characterised, it will be possible to determine the dominant starspot distribution.