I've prepared a small sample project which demonstrates how to make the cell's background Transparent when in edit mode for the Office_Black theme.
It involves creating a style for the TextBox control and editing the default control template of the GridViewCell element. The latter step involves editing the Edited visual state and setting the Background of the PART_CellBorder to Transparent.
Please have a look and let me know if such an approach would work for you. Please note that if you're using another theme, you should extract and modify the respective template accordingly.
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