a.nodeName is undefined Jquery error
The this keyword in your function does not refer to the element which was clicked on. By default it would refer to the highest element in the DOM, which would be the window.
To fix this you can use an unobtrusive event handler, instead of an outdated on* event attribute, as they run under the scope of the element which raised the event. Try this:
$("tr td img").click(deleteThisRow);
function deleteThisRow() {
$(this).closest('tr').fadeOut(400, function() {
$(this).remove();
});
}img {
width: 20px;
height: 20px;
border: 1px solid #C00;
}<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<table>
<tr>
<td>blah blah blah 1</td>
<td><img src="/whatever"></td>
</tr>
<tr>
<td>blah blah blah 2</td>
<td><img src="/whatever"></td>
</tr>
<tr>
<td>blah blah blah 3</td>
<td><img src="/whatever"></td>
</tr>
</table>