We report the magnetic properties of slightly electron-doped ${\text{Sm}}_{1\ensuremath{-}x}{\text{Ca}}_{x}{\text{MnO}}_{3}$ $(0.80\ensuremath{\le}x\ensuremath{\le}0.92)$. The Griffiths phase behavior in the inverse magnetic susceptibility was observed for $x\ensuremath{\ge}0.85$. The thermomagnetic irreversibility found in all samples could be explained according to the influence of martensitic strain on the magnetization behavior under various cooling histories. In the modified phase diagram, the low-field thermomagnetic irreversibility line passes through the region of Griffiths phase, indicating that the Griffiths phase is correlated with the accommodation strain. Our result indicates that the strain field, in addition to quenched disorders, may be an alternative approach to understand the observed Griffiths phase. Besides, the Griffiths phase itself is suggested to be insufficient for the appearance of colossal magnetoresistance effect in the present system.