I don't think there is an option to hide/remove fields from tooltip currently. Here is the idea shared on Power BI Ideas forum. You can vote it up and add your comments there to improve Power BI on this feature.
Just to close the loop on this. Since having a unique identifier was important for this graphic, I went into Excel and just added a counter row. Of course, I could have done it Power BI, but I can do it quicker in Excel.
Suggestion wise, it would be nice if Power BI allowed row number as a field/metric.