The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe thelong-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magneticfield. We show that in the presence of a strong helical forcing, the out-of-plane component ceases to behaveas a passive advected quantity and develops a nontrivial dynamics which deeply changes its large-scaleproperties. We show that a small-scale helicity injection correlates the input on the 2D component withthe one on the out-of-plane component. As a result, the third component develops a non-trivial energytransfer. The latter is mediated by homochiral triads, confirming the strong 3D nature of the leadingdynamical interactions. In conclusion, we show that the out-of-plane component in a 2D3C flow enjoysstrong non-universal properties as a function of the degree of mirror symmetry of the small-scale forcing.