Given a finite group $G$ with the identity $e$, the TI-power graph (trivial intersection power graph) of $G$ is an undirected graph with vertex set $G$, in which two distinct vertices $x$ and $y$ are adjacent if $⟨x⟩\cap ⟨y⟩=\{e\}$. In this paper, we obtain closed formulas for the metric and strong metric dimensions of the TI-power graph of a finite group. As applications, we compute the metric and strong metric dimensions of the TI-power graph of a cyclic group, a dihedral group, a generalized quaternion group, and a semi-dihedral group.