Magnetic nanoparticles (MNP) offer a large variety of promising applications in medicine thanks to their exciting physical properties, e.g., magnetic hyperthermia and magnetic drug targeting. For these applications, it is crucial to quantify the amount of MNP in their specific binding state. This information can be obtained by means of magnetorelaxometry (MRX), where the relaxation of previously aligned magnetic moments of MNP is measured. Current MRX with optically pumped magnetometers (OPM) is limited by OPM recovery time after the shut-off of the external magnetic field for MNP alignment, therewith preventing the detection of fast relaxing MNP. We present a setup for OPM-MRX measurements using a commercially available pulsed free-precession OPM, where the use of a high power pulsed pump laser in the sensor enables a system recovery time in the microsecond range. Besides, magnetometer raw data processing techniques for Larmor frequency analysis are proposed and compared in this paper. Due to the high bandwidth (≥100 kHz) and high dynamic range of our OPM, a software gradiometer in a compact enclosure allows for unshielded MRX measurements in a laboratory environment. When operated in the MRX mode with non-optimal pumping performance, the OPM shows an unshielded gradiometric noise floor of about 600 fT/cm/Hz for a 2.3 cm baseline. The noise floor is flat up to 1 kHz and increases then linearly with the frequency. We demonstrate that quantitative unshielded MRX measurements of fast relaxing, water suspended MNP is possible with the novel OPM-MRX concept, confirmed by the accurately derived iron amount ratios of MNP samples. The detection limit of the current setup is about 1.37 μg of iron for a liquid BNF-MNP-sample (Bionized NanoFerrite) with a volume of 100 μL.