I wonder if I might persuade the layout editor that the aesthetics would be improved if the underlining was removed?
Underlining is a holdover from the days of typewriters, and considered unaesthetic in professional typesetting [1, 2]. It's really only done in scripts, manuscripts and other non-published documents.
[1] https://practicaltypography.com/underlining.html
[2] https://writing.stackexchange.com/questions/4674/is-emphasiz...