The long-sought pair density wave (PDW) is an exotic phase of matter in which charge density wave (CDW) order is intertwined with the amplitude or phase of coexisting, superconducting order. Originally predicted to exist in copper-oxides, circumstantial evidence for PDW order now exists in a variety of materials. Recently, scanning tunneling microscopy (STM) studies have reported evidence for a three-component CDW at the surface of the heavy-fermion superconductor, UTe₂, persisting below its superconducting transition temperature [Aishwarya et al., Nature 618, 928933 (2023); Gu et al., Nature 618, 921927 (2023); LaFleur et al., Nat. Commun. 15, 4456 (2024)]. Here, we use hard x-ray diffraction measurements on crystals of UTe₂ at 𝑇 = 1.9 and 12 K to search for a bulk signature of this CDW. Using STM measurements as a constraint, we calculate the expected locations of CDW superlattice peaks and sweep a large volume of reciprocal space in search of a signature. We fail to find any evidence for a CDW near any of the expected superlattice positions in many Brillouin zones. We estimate an upper bound on the CDW lattice distortion of 𝑢_max≲4 ×10⁻³ Å. Our results suggest that the CDW observed in STM is either purely electronic, somehow lacking a signature in the lattice, or is restricted to the material surface.