Lemma C.1 in [R. Veltz and O. Faugeras, SIAM J. Math. Anal., 45(3) (2013), pp. 1527-1562] is wrong. This lemma is used in the proof of the existence of a smooth center manifold, Theorem 4.4 in [5]. An additional assumption is required to prove this existence. We spell out this assumption, correct the proofs and show that the assumption is satisfied for a large class of delay functions τ . We also weaken the general assumptions on τ .