Propagation of a H2-added strained laminar CH4/air flame in a rich-to-lean stratified mixture is numerically studied. The back-support effect, which is known to enhance the consumption speed of a flame propagating into a leaner mixture compared to that into a homogeneous mixture, is evaluated. A new method is devised to characterize unsteady reactant-to-reactant counterflow flames under transiently decreasing equivalence ratio, in order to elucidate the influence of flow strain on the back-support effect. In contrast to the conventional reactant-to-product configurations, the current configuration is more relevant to unsteady stratified flames back-supported by their own combustion products. Moreover, since H2 distribution downstream of the flame is known to play a crucial role in back-supported CH4/air flames, the influence of H2 addition in the upstream mixture is examined. The results suggest that a larger strain rate leads to a larger equivalence ratio gradient at the reaction zone through increased flow divergence, which amplifies the back-support. Meanwhile, since H2 addition in the upstream mixture does not affect the downstream H2 content, the relative increase in the consumption speed, i.e. the back-support, is suppressed with larger H2 addition. Especially, when the upstream H2 content decreases with the equivalence ratio, the H2 preferentially diffuses toward the unburned gas, which mitigates H2 accumulation in the preheat zone and further weakens the back-support.