"You deserve [every ounce of respect garnered]."
Everything inside the brackets is the direct object. In most grammars that are commonly used today, the direct object is a specific function in clause structure. (Aside: there is another function also called object which is used within the structure of a preposition phrase.) In your example, the object function is realized by the whole expression "every ounce of respect garnered". Here are some other somewhat related examples, with the direct object enclosed by brackets:
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".) You could also say that the participle is a modifier within the direct object.