She said to me, "I wrote a poem on the mother's day".

She told me that she had written a poem on the mother's day.

She told me that she wrote a poem on the mother's day.

She told me that she has written a poem on the mother's day.

None of these

In indirect speech, the past simple tense (wrote) changes to past perfect (had written).

Hence, the correct indirect sentence is: She told me that she had written a poem on the mother's day.