Do you mean in the game editor? You can click Remove in the character editor
https://raw.githubusercontent.com/cxong/cdogs-sdl/gh-pages/_posts/cdogs_nuklear_char_editor.gif

Please note that characters are referenced by index in the game, so it may mess up the missions if you delete characters in the middle. It's safer to ignore - there is no limit to the number of characters. There is a fix in the backlog #396

I mean in the saved characters you use when you play the game, the characters you customize before entering a quick play session

you can't delete those at the moment