Takeuchi was the only one who didn't accept the invitation.
Literal
Takeuchi only [topic-は] invitation [to-に] did-not-respond.
だけは combines the restrictive particle だけ ('only') with the topic-contrast particle は, creating the structure 'X-only [contrasting with everyone else]' — pointing Takeuchi out specifically as the exception. 招待に応じる = 'to accept/respond to an invitation' (応じる takes に for the thing being responded to).