In impunity games proposers, like allocators in dictator games, can take what they want; however, responders can refuse offers deemed unsatisfactory at own cost. We modify the impunity game via allowing offers to condition of another participant's counterfactual generosity intention. For a given pair of proposer candidates each states, via the strategy vector method, an intended and two adjusted offers: one (possibly) upward adjusted in case the intended offer of the other candidate is higher and one (possibly) downward adjusted in case it is lower. Additionally, each candidate determines an acceptance threshold for the responder role. Only one candidate in each pair is randomly selected and endowed as the actual proposer whose offer is either possibly upward or downward adjusted depending on the counterfactual offer of the other proposer candidate. The endowed proposer of one pair is matched with the non-endowed candidate of another pair in the responder role. The data confirm that counterfactual intentions of others often affect own generosity via substantial and significant average adjustments to the weakest social influence. Overall, offers seem correlated with acceptance thresholds. Furthermore, we find significant gender differences: female participants state lower intended and adjusted offers as well as acceptance thresholds and therefore appear to be less sensitive to social influence.