Checking if switch is checked and doing something with the data
With a function:

var checkedValue = function (tdid, field) {
    if ($("." + field + "-" + tdid).is(':checked')) {
        return $("." + field + "-text-" + tdid).text();
    }
    return "";
}


and you could then simply call that with:

for(var i = 0; i &lt; people_to_save_parse.length; i++) {
    people_to_save_parse[i].id = checkedValue(people[i].tdid, "ID");
    people_to_save_parse[i].firstname = checkedValue(people[i].tdid, "Name");
    people_to_save_parse[i].lastname = checkedValue(people[i].tdid, "Surname");
}


This removes much of the code duplication.

Note also that convention puts the { at the end of the line in JavaScript, not at the start of the next line. Also, you should add space between your operators and expressions to make them more readable. Finally, you don't need to add the == true as it is not useful in the if condition since the is(":checked") function returns a boolean already.

A concern I have is that you have two arrays, people_to_save_parse and people. You index them both with the same i index, and there is no apparent control that ensures they are 'in sync'. Are they a 1-to-1 matching pair of arrays?