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We present the analysis of 34 light curves in $V$ and $I$ of 17 giant stars in the globular cluster NGC 3201, to check if such stars are variable and if their variability has some kind of impact on the iron abundance as obtained from spectroscopic measurements. First, we computed the Generalized Lomb-Scargle and Phase Dispersion Minimization periodograms on the sample to check if the stars were variables. In this way, 7 stars of the sample were found to be non-variable, 2 stars are considered as possible variables, and 8 stars were found to be variable, with periods ranging from $0.0881\pm0.0001$ to $0.5418\pm0.0027$ days. According to the literature, the variables have distinct values of $\text{[Fe I/H]}$: the 3 most metal-rich stars are in the RGB stage, one has an $\text{[Fe I/H]}=-1.37$ dex, while the other two have $\text{[Fe I/H]}=-1.31$ dex. The two most metal-poor variables have $\text{[Fe I/H]}=-1.61$ dex and $\text{[Fe I/H]}=-1.62$ dex, and are AGB stars; the remaining variables have $\text{[Fe I/H]}=-1.44$, $-1.48$, and $-1.50$ dex, the first two being RGB while the last is AGB star. On the other hand, stars that appear to be non-variables have $-1.56\leq\text{[Fe I/H]}\leq-1.40$. We conclude that variability somehow affects the spectroscopic determination of the iron content of giant stars in NGC 3201 increasing the iron spread of the cluster. If variability is not taken into account, this spread could be wrongly interpreted as due to an intrinsic iron spread affecting the stars of the cluster.