Motivated by the recent observations of $T^*_{cs0}(2870)^0$, $T^*_{c\bar s 0}(2900)^0$ and $T^*_{c\bar s 0}(2900)^{++}$ open-charmed tetraquark states by LHCb, we study the decays of heavy mesons to these open-charmed tetraquark states ($T$) using a topological amplitude approach. We first obtain the $T\to DP$ and $DS$ strong decay amplitudes by decomposing them into several topological amplitudes, where $P$ is a light pseudo-scalar particle and $S$ is a low-lying scalar particle.
Subsequently, weak decay amplitudes of $\overline B\to D\overline T$, $\overline D T$ and $\overline B\to TP$, $TS$ decays are decomposed topologically.
In addition, $B^-_c\to T\overline T$ decays are also discussed. Using these results, modes with an unambiguous exotic interpretation in flavor are highlighted.