Instead of using
just use a space:
@Ajax.ActionLink(" ","Delete", "FinancialIntermediary", new { id = item.FinancialIntermediaryID }, new AjaxOptions { HttpMethod = "GET", OnSuccess = "DeleteSuccessFI", Confirm = "are you sure to perform the deletion." },new { @class="classname" })
You'd also need to make some space for your element so the background-image can be shown:
.classname
{
background-image:url('../../Images/delete.png');
display: inline-block;
width: 20px; /* adjust as necessary */
height: 10px;/* adjust as necessary */
}