。
She accepted our invitation.
Literal
She [topic-は] our invitation [to-に] responded.
応じる ('to respond, to comply with, to accept') takes に to mark what one is responding to — '~に応じる' = 'respond to ~ / accept ~.' The verb has a slightly formal feel, common in writing about social and business interactions. For an invitation specifically, 招待に応じる ('accept an invitation') is the standard collocation; the more casual equivalent in spoken language is 招待を受け入れる or simply 来てくれる.