Can I ask my friend to change a poem that uses details from our private conversation?

My friend sent the poem she planned to read at an open mic. The line about leaving a flat with a kettle and one blue shoe was from something I'd told her after a breakup.

She'd changed the name and the city. She says nobody will know it's me. Several mutual friends are going to the reading, and two helped me move that day. They would recognise the shoe.

I hadn't asked her to keep the conversation secret; I thought telling a friend was different from providing material for a public poem. She says the image matters to the ending, and removing it will make the piece weaker.

I like her writing and don't want to police everything that inspires it. What can I reasonably ask her to change when the detail matters to both the poem and my wish not to become identifiable at the reading?