Someone or something (subject) must do something (verb). Sometimes, the subject does something to something else—that other thing is called the object. Objects receive the action of the verb. Objects can be direct and/or indirect. John carried the bag. John is the subject. He is the doer, the actor, in the sentence. Carried is the verb.
An indirect object exists in a sentence alongside a direct object. They refer to someone, or something, directly impacted by the subject of a sentence's specific enactment of a verb. Every
Indirect object is a grammatical function. The grammatical forms that can function as the indirect object in English grammar are noun phrases including pronouns, prepositional phrases, verb phrases, and noun clauses. Indirect objects are constituents of the predicate. Sentences with indirect objects must also have direct objects.
Direct Object: A direct object is a noun or pronoun that receives the action in a sentence. A direct object answers the question “what or who?”. Indirect Object: Indirect objects are noun or pronouns in a sentence that identifies to whom or for whom the action of the verb is performed, as well as who is receiving the direct object. Read
And so, to answer your question: in your example the participle isn't modifying the direct object, and that is because the participle is actually part of the direct object. (You could say that the participle is a modifier, and it is modifying the noun "respect" which is the head of the complement (object) of a preposition phrase headed by "of".)
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direct indirect object examples