Extending partial edge colorings

We consider the problem of extending partial edge colorings of (iterated) cartesian products of even cycles and paths, focusing on the case when the precolored edges constitute a matching. We prove the conjecture of Casselgren, Granholm and Petros that a precolored distance 3 matching in the Cartesian product of two even cycles can be extended to a 4-coloring of the edge set of the whole graph. Actually, a generalization for the Cartesian product of two bipartite graphs is proved.