Get rid of "search" button?

I'm trying to make a web-site with a lot of info. Therefor I like to get rid of all redundant (non)info.

Inside the google bar, it already says what it is, so through block-settings I removed the title

But now I have it in my left column in two lines; first line the google bar and the second line the search button.

I don't need the search button, because all people who know only a little how to use a computer, are able to find the return key on their keyboard or similar function on cellular, iPad or whatever.

To get rid of it, mustn't be that a problem, but it would be nice if this option is added in the administration menu....