Line current differential relays (LCDRs) are measurement-driven relays that rely on time-synchronized multi-phase current waveforms to infer internal faults in AC and DC power networks. In inverter-based microgrids, however, the increasing reliance on digitally communicated measurements exposes LCDRs to false-data injection attacks (FDIAs), in which adversaries manipulate remote measurement streams to create protection-triggering yet physically inconsistent current trajectories. This paper addresses this emerging measurement integrity problem by introducing a measurement integrity validation scheme that operates as a supervisory instrumentation layer for modern LCDRs. The proposed scheme interprets short windows of synchronized instantaneous current measurements recorded during relay operation and assesses their physical consistency to distinguish genuine fault-induced trajectories from cyber-manipulated measurement streams. A recurrent neural network is trained offline using only relay-available current measurements and exploits the temporal structure of differential current waveforms, which remains informative in inverter-dominated systems where current magnitude is no longer a reliable observable. The method requires no additional sensors, auxiliary protection elements, or prior knowledge of network topology, and is applicable to both AC and DC LCDRs without structural modification. The proposed measurement validation scheme is evaluated on an islanded inverter-based microgrid under a comprehensive set of fault and FDIA scenarios, demonstrating high detection accuracy while preserving relay dependability. Hardware-in-the-loop validation using an OPAL-RT real-time simulator confirms that the scheme satisfies protection timing constraints and can operate in real time under realistic operating conditions.