The correct option is D they/us/them
In the first case, the subject of the verb are third persons. Hence, the subject pronoun is in third person plural, that is "they". If the pronoun is receiving the action, it is called a direct object. Object pronouns are always used when the antecedent is a direct object. Here, the speaker(s) are invited to stay, with the third persons. The object pronoun for first person plural is "us" and for third person plural is "them", irrespective of gender. Hence, Option D is correct. The rest of the options do not adhere to this rule, hence incorrect.