We study the quantum nonlinear Hall effect in two-dimensional (2D) materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. Candidate 2D materials to observe this effect are two-dimensional transition metal dichalcogenides (TMDCs). First, we use an ab initio based tight-binding approach to demonstrate that monolayer T-d-structure TMDCs exhibit a finite Berry curvature dipole. In the 1H and 1T' phase of TMDCs, we show the emergence of a finite Berry curvature dipole with the application of strain and an electrical displacement field, respectively.