If you don't have it under String Translation, it means you did not set any text and link for the Action Button under Theme options > Header & Subheader > Extras section. It is necessary if you want WPML plugin to see this text.
Yes, this is true. It is not possible to save empty field (but you can disable WPML for a while, save empty field and then activate plugin again). However, if you do not have the text we marked on screenshot, you should remove whole WPML plugin and then install it again. But if this won't help, please contact with wpml support team and ask them what might be the reason because we checked those texts and everything is fine.
Comments
please change String Translation once again but this time more carefully as this text is there for sure.