You can't easily. You can try:
- Page Viewer Web Part, and just consume the library from Subsite A. When setting up the URL to the page, include IsDlg=1 at the end, that'll hide the ribbon and stuff: http://davidlozzi.com/2014/03/25/we-all-know-what-sharepoint-isdlg-does-wait-what-the/
- Custom web part which pulls and reads the library, but you would have to recreate almost all the functionality around a library's UI (terrible idea)
- Use CQWP as you tried before, and live with the links ;) it's all in SharePoint anyway.
Using the first option, you could embed this on your page, ensure you have jQuery in there:
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script type="text/javascript">
_spBodyOnLoadFunctionNames.push("hideItAll");
function hideItAll(){
if(window.location.search.toLowerCase().indexOf("isdlg=1") > 0){
$("#s4-ribbonrow").hide(); //ribbon bar
//because the bar joins us late in the game, we need to throw CSS in to hide it
$("head").append("<style>#Hero-WPQ2 { display:none }</style>");
$("#CSRListViewControlDivWPQ2").hide(); //views and search bar
}
}
</script>
Not sure how much you want to hide here, so i put it all in, remove what you'd like. Also you may have to check the second two IDs, that end in WPQ2, yours may be WPQ1 or 3? If you need help, you can use your dev toolbar to find your IDs, more help here: http://davidlozzi.com/2013/05/08/a-non-developers-intro-to-the-developer-toolbar-element-inspection/