[jquery] Is it possible to override / remove background: none!important with jQuery?

Any !important can be overridden by another !important, the normal CSS precedence rules still apply.

Example:

#an-element{
    background: #F00 !important;
}
#an-element{
    background: #0F0 !important; //Makes #an-element green
}

Then you could add a style attribute (using JavaScript/jQuery) to override the CSS

$(function () {  
    $("#an-element").attr('style', 'background: #00F !important;');
    //Makes #an-element blue
});

See the result here