Lately, the LHCb Collaboration reported the discovery of two new states in the B^+rightarrow D^+D^- K^+ decay, i.e., X_0(2866) and X_1(2904). In the present work, we study whether these states can be understood as {bar{D}}^*K^* molecules from the perspective of their two-body strong decays into D^-K^+ via triangle diagrams and three-body decays into {bar{D}}^*Kpi . The coupling of the two states to {bar{D}}^*K^* are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the X_0(2866) state, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large {bar{D}}^*K^* component in its wave function. On the other hand, the strong decay width for the X_1(2904) state, much smaller than its experimental counterpart, effectively rules out its assignment as a {bar{D}}^*K^* molecule.