Martha is best known for her oatmeal cookies.
Michelle is best known for her oatmeal cookies.
The antecedent noun that agrees with the pronoun in this sentence is Martha or Michelle (if its a feminine )
A pronoun takes place of a noun to avoid repetition
The pronoun that follows a feminine noun is usually She, her etc
The pronoun that follows a masculine noun is usually he, him etc
The pronoun that follows two or more nouns is usually they, their
From the options,
We cannot use The Smiths as the antecedent noun else it would have been their oatmeal cookies
We cannot use Jim Avery else it would have been his oatmeal cookies
We can either use Martha or Michelle(as a feminine name), as the are both singular feminine nouns and can have their pronoun as her oatmeal cookies in the sentence.
See more about pronoun her:https://brainly.com/question/15458544