Use two classes :

<style type="text/css">
    .RadWindow .rwWindowContent .radalert {
         background-image:url("images/InfoImg.png"); 
    }
    .RadWindow.newbg .rwWindowContent .radalert {
         background-image:url("images/other_image.png"); 
    }
</style>

JS:

$('.RadWindow').addClass('newbg');    // adds the new background
$('.RadWindow').removeClass('newbg'); // removes the new background
$('.RadWindow').toggleClass('newbg'); // toggles the new background

let suppose you have to change the url of the image to "images/InfoImg2.png" you can use the code option 1-

jQuery -

var newUrl = "images/InfoImg2.png";
$(".radalert").css({
    backgroundImage : 'url("'+newUrl+'")'
});

OR

CSS -

RadWindow .rwWindowContent .radalert2{
  background-image:url("images/InfoImg2.png"); 
}

jQuery -

$(".radalert").addClass("radalert2");

Try

$('.RadWindow .rwWindowContent .radalert').css('background-image', 'images/new.png')

Try this simple old fashioned method:

$(document).ready(function(){
    $('.RadWindow .rwWindowContent .radalert')
    .css('background-image', "url('images/InfoImg.png')");
})

OR

as per comment request, you could make use of jQuery's .toggleClass() method. To make best advantage, simple set 2 alternating background classes in css. Assign one to your element on load (write it in the HTML) and simply have the other one ready. Then, on an "action", use toggleClass to alternate the two classes!

Working Example

How it works is simple. First set up your CSS:

<style type="text/css">
    .bg-type-01 {
        background-image: url("some url");
    }
    .bg-type-02 {
        background-image: url("another url");
    }
</style>

Then apply your first class to your element:

<div class="radalert bg-type-01"> ... </div>

Finally, write the very simple JS with jQuery!

<script type="text/javascript">
    $(function() {
        $("something").on("click", function(e) {
            $(".radalert").toggleClass("bg-type-01 bg-type-02");
        });
    })
</script>