Electrical interference from various sources is a common issue for experimental extracellular electrophysiology recordings collected using multi-electrode array neural recording systems. This interference deteriorates the signal-to-noise ratio (SNR) of the raw electrophysiology signals and hampers the accuracy of data post-processing using techniques such as spike-sorting. Traditional signal processing methods to digitally remove electrical interference during post-processing include bandpass filtering to limit the signal to the relevant spectral range of the biological data, e.g., the spikes band (300 Hz - 7 kHz), targeted notch filtering to remove power line interference from standard alternating current mains electricity and common reference removal to minimize noise common to all electrodes. These methods require a priori knowledge of the frequency of the interfering signal source to address the unique electromagnetic interference environment of each experimental setup. We discuss an adaptive method for automatically removing narrow-band electrical interference through a spectral peak detection and removal (SPDR) step that can be applied during post-processing of the recorded data, based on the intuition that tall, narrowband signals localized in the signal spectrum correspond to interference, rather than the activity of neurons. A spectral peak prominence (SPP) threshold is used to detect these peaks in the frequency domain, which will then be removed via notch filtering. We applied this method to simulated waveforms and also experimental electrophysiology data collected from cerebral organoids to demonstrate its effectiveness for removing unwanted interference without significantly distorting the neural signals. We discuss that proper selection of the SPP threshold is required to avoid over-filtering, which can result in distortion of the electrophysiology data. We also compare the firing-rate activity in the filtered electrophysiology with fluorescence calcium imaging, a secondary cellular activity marker, to quantify signal distortion and provide bounds on SNR-based optimization of the SPP threshold. The adaptive filtering technique demonstrated in this paper is a powerful method that can automatically detect and remove interband interference in recorded neural signals, potentially enabling data collection in more naturalistic settings where external interference signals are difficult to eliminate.