Abstract: Light primordial black holes (PBHs) with masses smaller than 10(9) g (10(-24) M-circle dot) evaporate before the onset of Big-Bang nucleosynthesis, rendering their detection rather challenging. If efficiently produced, they may have dominated the universe energy density. We study how such an early matter-dominated era can be probed successfully using gravitational waves (GW) emitted by local and global cosmic strings. While previous studies showed that a matter era generates a single-step suppression of the GW spectrum, we instead find a double-step suppression for local-string GW whose spectral shape provides information on the duration of the matter era. The presence of the two steps in the GW spectrum originates from GW being produced through two events separated in time: loop formation and loop decay, taking place either before or after the matter era. The second step – called the knee – is a novel feature which is universal to any early matter-dominated era and is not only specific to PBHs. Detecting GWs from cosmic strings with LISA, ET, or BBO would set constraints on PBHs with masses between 10(6) and 10(9) g for local strings with tension G μ= 10(-11), and PBHs masses between 10(4) and 10(9) g for global strings with symmetry-breaking scale eta = 10(15) GeV. Effects from the spin of PBHs are discussed.