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Gamma-ray burst (GRB) 190114C was a bright burst that occurred in the local Universe ( z  = 0.425). It was the first GRB ever detected at teraelectronvolt (TeV) energies, and this was thanks to MAGIC. We characterize the ambient medium properties of the host galaxy through the study of the absorbing X-ray column density. Using a combination of Swift , XMM-Newton , and NuSTAR observations, we find that the GRB X-ray spectrum is characterized by a high column density that is well in excess of the expected Milky Way value and decreases, by a factor of ∼2, around ∼10 5 s. Such a variability is not common in GRBs. The most straightforward interpretation of the variability in terms of the photoionization of the ambient medium is not able to account for the decrease at such late times, when the source flux is less intense. Instead, we interpret the decrease as due to a clumped absorber, denser along the line of sight and surrounded by lower-density gas. After the detection at TeV energies of GRB 190114C, two other GRBs were promptly detected. These two also have high intrinsic column density values, and there are hints for a decrease in their column densities as well. We speculate that a high local column density might be a common ingredient of TeV-detected GRBs.