If you have a few minutes... you could try suppressing that part of the page with a custom style rule. For example:

@namespace url(http://www.w3.org/1999/xhtml);
@-moz-document domain("www.msn.com") {
  #subfoot {display:none !important}
}

There are two ways to apply that.

(1) A userContent.css file (info on how to create/edit that file in this post: https://support.mozilla.org/questions/949106#answer-404166)

(2) A userstyle in the Stylish extension (info on how to create a rule in Stylish in this post: https://support.mozilla.org/questions/934019#answer-358059)

The above rule also removes the normal search box at the bottom of the screen since it seemed more reliable to target the whole area. If you want to be a bit more surgical, try this rule instead:

@namespace url(http://www.w3.org/1999/xhtml);
@-moz-document domain("www.msn.com") {
  #ls1, #subfoot > div:nth-of-type(2) {display:none !important}
}

That targets the moving box by its current id (as I see it) and also by its position as the second division in the subfoot (in case the id changes frequently).

In my case that is doable with Adblock Plus. Just block that popup with a right click. Or close it, the popup has an "x", it should not come up again if you allow to save cookies on that site IMO.