JSFiddle - React, Tailwind, and code Playground

JavaScript

Date.prototype.getWeek = function () {
    var onejan = new Date(this.getFullYear(), 0, 1);
    return Math.ceil((((this - onejan) / 86400000) + onejan.getDay() + 1) / 7);
}

var arr = [{
    "StudentID": 5041,
        "Status": "Joshua picked up  from school [0]    at 12:41PM and reached home [0] at    12:43PM",
        "Date": "2013-11-20"
}, {
    "StudentID": 5042,
        "Status": "Joshua picked up  from school [0]    at 12:41PM and reached home [0] at    12:43PM",
        "Date": "2013-11-20"
}, {
    "StudentID": 5043,
        "Status": "Joshua picked up  from school [0]    at 12:41PM and reached home [0] at    12:43PM",
        "Date": "2013-11-20"
}];


var todayWeekNo = new Date().getWeek();
$.each(arr, function (i, j) {
    var isEqual = todayWeekNo == new Date(j.Date).getWeek();
    if (isEqual) {
        delete arr[i];
    }
});
console.log("arr", arr);