What is the function of the complement shown in parentheses in this sentence Susan baked Steve and Tim a fresh apple pie?

The noun 'pie' is not a complement.

In the given sentence, the noun 'pie' is the direct object of the verb 'baked'.

The complete direct object is the noun phrase 'a fresh Apple pie'.

A complement can be a subject complement or an object complement.

A subject complement is a noun or an adjective that follows a linking verb and restates the subject of the sentence, for example:

• "Dessert was a fresh Apple pie." (dessert = pie, a noun)
• The fresh Apple pie was delicious. (pie = delicious, an adjective)

An object complement is a noun that follows a direct object and restates it, for example:

• Susan served dessert, a fresh Apple pie. (the noun 'pie' restates the direct object 'dessert' / dessert = pie)