This paper assesses the efficacy of Index Modulated (IM) schemes within Orthogonal Frequency Division Multiplexing (OFDM) systems under the influence of Narrowband Interference (NBI). Moreover, a novel mitigation strategy leveraging compressive sensing (CS) is introduced for OFDM-IM systems. The findings demonstrate that in contrast to conventional OFDM, OFDM-IM displays notable resilience against NBI up to a signal-to-narrowband interference ratio (SNIR) of -15dB. The expansion of NBI bandwidth exhibits a limited impact on performance degradation, whereas heightened interference power exerts a more pronounced effect. Broadly, in the absence of mitigation measures, error performance deteriorates and eventually stabilizes even at elevated SNR levels. Notably, under conditions of substantial interference power, the CS-driven NBI cancellation technique enhances the performance of OFDM-IM schemes, resulting in a substantial reduction of the error floor.