Temporal Networks with Uncertainty are a powerful and widely used formalism for representing and reasoning over temporal constraints in the presence of uncertainty. Since their introduction, they have been used in planning and scheduling applications to model situations where some activity durations or event timings are not under the control of the scheduling agent. Moreover, a wide variety of classes of temporal networks (depending on the types of constraints) have been defined, and many algorithms for dealing with these emerged. We are interested in the repair problem, consisting of reconsidering the bounds of the uncertain durations when the network is not controllable, i.e., when no strategy for scheduling exists. This problem is important, as it allows for the explanation and negotiation of the problematic uncertainties. In this paper, we address the repair problem for a very expressive class of temporal networks, namely the Disjunctive Temporal Networks with Uncertainty. We use the Satisfiability Modulo Theory framework to formally encode and solve the problem, and we devise a uniform solution encompassing different "levels" of controllability, namely strong and weak. Moreover, we provide specialized encodings for important subclasses of the problem, and we experimentally evaluate our approaches.