What is happening is totally normal. You append a link and the the link is appended. If I get it right, what you want is to display an image (with a link) whenever a user hovers over you grid content. I suppose this is what you are looking for:
Jquery:
$(document).ready(function(){
$("#contentDiv").hover(function(){
$("#imageDiv").html("<a href='yourlink.com'><img src='yourimage.png'</a>");
$("#imageDiv").show();
}, function(){
$("#imageDiv").hide();
});
$("#contentDiv").mouseout(function(){
$("#imageDiv").hide();
});
});
HTML displayed in your grid (each row):
<div id="imageDiv">
</div>
<div id="contentDiv">
Testing content, supposing is displayed in your grid
</div>
You can also check it out in this fiddle. You could play with your test div dimensions and the picture to make it hover in a more stable fashion. I am just pointing out the idea.
Hope I helped!