On the third homotopy group of Orr's space

K. Orr defined a Milnor-type invariant of links that lies in the third homotopy group of a certain space $K_{\omega }\mathrm{.}$ The problem of non-triviality of this third homotopy group has been open. We show that it is an infinitely generated group. The question of realization of its elements as links remains open.