Change Markup in array

I am trying to add the shortcode into a form for a share email. Using the

[user_favorites]

This outputs but I would like a different markup for a list of titles and small thumbnail images

We are using the current markup for the favorites with the shortcode in a listing already and I don’t need to alter this.

Is there a way to jump into the code of the shortcode and output this markup differently?
I have tried to create a custom shortcode using the favorite array but it still outputs the same markup using:

get_user_favorites($user_id = null, $site_id = null, $filters = null);

Any suggestions or pointers here would be greatly appreciated.