I currently use the striking search widget with an empty title on page and blog widget areas. Every time I make a change in the header or home page widget areas (e.g. remove or add a widget) the title "Search" is automatically added to the striking Search widget.
While it is not a critical issue it requires to always remember to clean the search title after making changes to other widgets.
Many thanks for the test and response. It could then be also related to the 2nd component/plugin in WPML - the string translations. I will have a look. You can now close this issue.