You can use the CSS tag display: noneand then remove the tag when you click the button and add the tag back when you finish sharing on Twitter.
Something like that:
HTML
<input type="button" class="clickMe" value="Click Me" />
<img src="img/twitter.png" class="twitterPic hideMe" />
CSS
, .
.hideMe { display: none;}
JavaScript
$(".clickMe").on("click", function () {
$(".twitterPic").removeClass("hideMe");
});
JQuery :
https://api.jquery.com/removeClass/
https://api.jquery.com/addClass/