In the more general setting of a symmetric monoidal category $\mathsf{M}$ and a general colored operad $\mathsf{O}$, the structure of an $\mathsf{O}$-algebra $X$ regarded as a $\mathsf{WO}$-algebra is described explicitly in the book Homotopical Quantum Field Theory (called HQFT below), Corollary 7.2.9. The arxiv version is here. When $\mathsf{M}$ is a suitable category of topological spaces $\mathsf{Top}$, this pullback algebra structure is as Bertram Arnold described in the comments above, where you first forget about the edge lengths. In the general context of $\mathsf{M}$, the interval $[0,1]$ is replaced by a commutative segment $\mathsf{J}$ (Definition 6.2.1 in HQFT), which provides a notion of homotopy and comes with a counit map to the monoidal unit of $\mathsf{M}$. In $\mathsf{Top}$, this counit is $[0,1] \to *$.

To understand Corollary 7.2.9, you will first need to read Theorem 7.2.1 in HQFT, which explicitly describes the structure of a $\mathsf{WO}$-algebra using the formalism of trees and commutative segment. That theorem is one way to formally say that a $\mathsf{WO}$-algebra is an $\mathsf{O}$-algebra up to homotopy. In HQFT Definition 6.3.1, the Boardman-Vogt construction $\mathsf{WO}$ is defined as an entrywise coend indexed by a parameter category built from trees. You can apply that definition and the results mentioned above to the little 2-cube operad or any other operad. A number of examples can be found in HQFT.