Accoring to the vim documentation t_Cs and t_Ce can be set to for undercurl start/end respectively. However, doing that in .vimrc seems to have no effect when used in a highlighting style, in terminal vim.

Minimal vimrc

let &t_Cs = "\e[6m"
let &t_Ce = "\e[24m"
hi SpellBad     gui=undercurl guisp=red term=undercurl cterm=undercurl

However, the bad spelling highlighting still uses underlines, despite the above settings. I assume this is because somewhere undercurl is hard coded to be GUI only. Can this be changed, please? I have created a terminal that allows undercurl highlighting. https://github.com/kovidgoyal/kitty

Also, guisp will need to be passed to the terminal as well, so probably there needs to be another termcap setting, maybe t_8u that will work like the existing t_8f and t_8b settings.