We consider an optimal control problem of tracking type governed by a time-discrete regularized phase-field fracture or damage propagation model. The energy minimization problem describing the fracture process is formulated by the corresponding Euler-Lagrange equations that contain a regularization term that penalizes the violation of the irreversibility condition in the evolution of the fracture. We prove convergence of solutions of the regularized problem when taking the limit with respect to the penalty term and obtain an estimate for the constraint violation in terms of the penalty parameter. To this end, we make use of convexity of the energy functional due to a viscous regularization which corresponds to a time-step restriction in the temporal discretization of the problem. Numerical experiments underline our theoretical findings.