GNU standards: What should happen with illegal option?

[Jeffrey Walton]

The GNU standard for --version and --help says the program should
write to standard output and exit with success. Cf.,
https://www.gnu.org/prep/standards/html_node/_002d_002dhelp.html#g_t_002d_002dhelp

What happens with an illegal option that the program rejects and
exits? Does the message get written to standard output or standard
error? Should the program exit with an error? (I'm fairly certain it
should exit with an error, but I can't tell where the message should
be printed).

If the information could be added to
https://www.gnu.org/prep/standards/html_node/Command_002dLine-Interfaces.html,
then it would be greatly appreciated.

Jeffrey Walton
Baltimore, MD, US