The simple temporal problem (STP) and its generalization allowing disjunctive constraints (DTP) are some of the most influential reasoning formalisms for temporal information in AI. We study the problem of resolving inconsistency of data encoded in the DTP, i.e. given a DTP instance, find the minimum number of constraints to remove to make it satisfiable. While this problem is NP-hard in general, it is reasonable to assume that the amount of erroneous data will be small in practical instances. We therefore study the parameterized complexity of this problem parameterized by the number of constraints to be removed to achieve satisfiability, and obtain full P/NP-hard and FPT/W[1]-hard dichotomies for all binary DTP languages.