Let $(N,h)$ be a compact smooth Riemannian manifold, and let $B(0,1) \subset \mathbb{R}^2$ denote the open unit disk. Suppose $u \in W^{1,2}_{\mathrm{loc}}(B(0,1)\setminus\{0\};N)$ is a weakly harmonic map which is smooth on $B(0,1)\setminus\{0\}$. If $u$ has finite Dirichlet energy,
where $|du|$ is computed using the Euclidean metric on $\mathbb{R}^2$ and the Riemannian metric $h$ on $N$, then there exists a smooth harmonic map $\tilde u: B(0,1) \to N$ such that $\tilde u = u$ on $B(0,1)\setminus\{0\}$.