The only way to remove the YouTube branding (while keeping the video clickable) is to place the embed iFrame inside a container that has overflow
set to hidden
and has a slightly smaller height than the iFrame.
Of course this means the bottom of your video gets chopped off.
Also, you will be most likely breaching YouTube's Terms of Service.
CSS:
.videoWrapper {
width: 550px;
height: 250px;
overflow: hidden;
}
HTML:
<div class="videoWrapper">
<iframe width="550" height="314" src="https://www.youtube.com/embed/vidid?modestbranding=1&rel=0&showinfo=0" frameborder="0" allowfullscreen></iframe>
</div>