Galaxies and galaxy groups located along the line of sight towards gravitationally lensed quasars produce high-order perturbations of the gravitational potential at the lens position. When these perturbation are too large, they can induce a systematic error on $H_0$ of a few-percent if the lens system is used for cosmological inference and the perturbers are not explicitly accounted for in the lens model. In this work, we present a detailed characterization of the environment of the lens system WFI2033-4723 ($z_{rm src} = 1.662$, $z_{rm lens}$ = 0.6575), one of the core targets of the H0LICOW project for which we present cosmological inferences in a companion paper (Rusu et al. 2019). We use the Gemini and ESO-Very Large telescopes to measure the spectroscopic redshifts of the brightest galaxies towards the lens, and use the ESO-MUSE integral field spectrograph to measure the velocity-dispersion of the lens ($sigma_{rm {los}}= 250^{+15}_{-21}$ km/s) and of several nearby galaxies. In addition, we measure photometric redshifts and stellar masses of all galaxies down to $i < 23$ mag, mainly based on Dark Energy Survey imaging (DR1). Our new catalog, complemented with literature data, more than doubles the number of known galaxy spectroscopic redshifts in the direct vicinity of the lens, expanding to 116 (64) the number of spectroscopic redshifts for galaxies separated by less than 3 arcmin (2 arcmin) from the lens. Using the flexion-shift as a measure of the amplitude of the gravitational perturbation, we identify 2 galaxy groups and 3 galaxies that require specific attention in the lens models. The ESO MUSE data enable us to measure the velocity-dispersions of three of these galaxies. These results are essential for the cosmological inference analysis presented in Rusu et al. (2019).
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