Do you have develop fb like box before? If does't having yet, you can develop it on Facebook Developer site. After completely develop, then you can see fb like box with the border something like this:

Remove that border with adding "border_color = 'white'". Below is the full code example:

<div class="fb-like-box" 
data-href="http://www.facebook.com/platform" 
data-width="292" 
data-show-faces="true" 
data-stream="false" 
data-header="false"
border_color ="white"></div>

Then it will be display fb like box without border as below:



Done.