。
She invited me to dinner.
Literal
She [topic-は] me [object-を] meal [to-に] invited [for my benefit-てくれた].
招く ('to invite') takes the invitee with を and the event with に — 食事に招く ('invite to a meal'), パーティーに招く ('invite to a party'). The に marks the event as the destination of the invitation, parallel to its destination-marking use with motion verbs (学校に行く 'go to school'). The benefactive ~てくれる frames the act as a kindness done for the speaker.