Strong reciprocity is characterized by the willingness to altruistically reward cooperative acts and to altruistically punish norm-violating, defecting behaviours. Recent evidence suggests that subtle reputation cues, such as eyes staring at subjects during their choices, may enhance prosocial behaviour. Thus, in principle, strong reciprocity could also be affected by eye cues. We investigate the impact of eye cues on trustees' altruistic behaviour in a trust game and find zero effect. Neither the subjects who are classified as prosocial nor the subjects who are classified as selfish respond to these cues. In sharp contrast to the irrelevance of subtle reputation cues for strong reciprocity, we find a large effect of explicit, pecuniary reputation incentives on the trustees' prosociality. Trustees who can acquire a good reputation that benefits them in future interactions honour trust much more than trustees who cannot build a good reputation. These results cast doubt on hypotheses suggesting that strong reciprocity is easily malleable by implicit reputation cues not backed by explicit reputation incentives.