Methods for parameter estimation of gravitational-wave data assume that detector noise is stationary and Gaussian. Real data deviates from these assumptions, which causes bias in the inferred parameters and incorrect estimates of the errors. We develop a sensitive test of non-Gaussianity for real gravitational-wave data which measures meaningful parameters that can be used to characterize these effects. As a test case, we investigate the quality of data cleaning performed by the LIGO-Virgo-KAGRA collaboration around GW200129, a binary black hole signal which overlapped with the noise produced by the radio frequency modulation. We demonstrate that a significant portion of the non-Gaussian noise is removed below 50 Hz, yet some of the noise still remains after the cleaning; at frequencies above 85 Hz, there is no excess noise removed. We also show that this method can quantify the amount of non-Gaussian noise in continuous data, which is useful for general detector noise investigations. To do that, we estimate the difference in non-Gaussian noise in the presence and absence of light scattering noise.