Thermoplastic composite organosheets (OSs) are increasingly recognized as a viable solution for automotive and aerospace structures, offering a range of benefits including cost-effectiveness through high-rate production, lightweight design, impact resistance, formability, and recyclability. This study examines the impact response, post-impact strength evaluation, and hot-pressing repair effectiveness of woven glass fiber nylon composite OSs across varying impact energy levels. Experimental investigations involved subjecting composite specimens to impact at varying energy levels using a drop-tower test rig, followed by compression-after-impact (CAI) tests. The results underscore the exceptional damage tolerance and improved residual compressive strength of the OSs compared to traditional thermoset composites. This enhancement was primarily attributed to the matrix’s ductility, which mitigated transverse crack propagation and significantly increased the amount of absorbed energy. To mitigate impact-induced damage, a localized hot-pressing repair approach was developed. This allowed to restore the post-impact strength of the OSs to pristine levels for impact energies below 40 J and by 83.6% for higher impact energies, when OS perforation was observed. The measured levels of post-repair strength demonstrate a successful restoration of OS strength over a wide range of impact energies, and despite limitations in achieving complete strength recovery above 40 J, hot-pressing repair emerges as a promising strategy for ensuring the longevity of thermoplastic composites through repairability.