Mesenchymal stromal cells (MSCs) can be isolated from various tissues of healthy or patient donors to be retransplanted in cell therapies. Because the number of MSCs obtained from biopsies is typically too low for direct clinical application, MSC expansion in cell culture is required. However, ex vivo amplification often reduces the desired MSC regenerative potential and enhances undesired traits, such as activation into fibrogenic myofibroblasts. Transiently activated myofibroblasts restore tissue integrity after organ injury by producing and contracting extracellular matrix into scar tissue. In contrast, persistent myofibroblasts cause excessive scarring-called fibrosis-that destroys organ function. In this review, we focus on the relevance and molecular mechanisms of myofibroblast activation upon contact with stiff cell culture plastic or recipient scar tissue, such as hypertrophic scars of large skin burns. We discuss cell mechanoperception mechanisms such as integrins and stretch-activated channels, mechanotransduction through the contractile actin cytoskeleton, and conversion of mechanical signals into transcriptional programs via mechanosensitive co-transcription factors, such as YAP, TAZ, and MRTF. We further elaborate how prolonged mechanical stress can create persistent myofibroblast memory by direct mechanotransduction to the nucleus that can evoke lasting epigenetic modifications at the DNA level, such as histone methylation and acetylation. We conclude by projecting how cell culture mechanics can be modulated to generate MSCs, which epigenetically protected against myofibroblast activation and transport desired regeneration potential to the recipient tissue environment in clinical therapies.