In recent years, the changing landscape for the conduct and assessment of research and of researchers has increased scrutiny of the reward systems of science. In this context, correcting the research record, including retractions, has gained attention and space in the publication system. One question is the possible influence of retractions on the careers of scientists. It might be assessed, for example, through citation patterns or productivity rates for authors who have had one or more retractions. This is an emerging issue today, with growing discussions in the research community about impact. We have explored the influence of retractions on grant review criteria. Here, we present results of a qualitative study exploring the views of a group of six representatives of funding agencies from different countries and of a follow-up survey of 224 reviewers in the US. These reviewers have served on panels for the National Science Foundation, the National Institutes of Health, and/or a few other agencies. We collected their perceptions about the influence of self-correction of the literature and of retractions on grant decisions. Our results suggest that correcting the research record, for honest error or misconduct, is perceived as an important mechanism to strengthen the reliability of science, among most respondents. However, retractions and self-correcting the literature at large are not factors influencing grant review, and dealing with retractions in reviewing grants is an open question for funders.