antikaleo describes inviting someone back in return, in the context of reciprocal hospitality.

The attested use describes a return invitation: those invited to a meal may invite their host back, resulting in repayment.

1. Invite back as a return for hospitality · dominant

   In Luke 14:12, the aorist active subjunctive plural form occurs in the warning that friends, relatives, and wealthy neighbors might respond to a meal invitation by inviting the host back. The APB renders the clause, “lest they also invite you in return and you be repaid.”

   Luke 14:12

In the Anselm Project Bible: In Luke 14:12, the APB presents the action as “invite you in return” within a warning about being repaid.