You access it using Request.Form as you currently are, the issue might be the fact that you're giving the component a "name" in the element and then attaching a different "name" via attr. Try removing one of the name allocations
function CreateTextbox(){
var $ctrl = $('<input id="txtExtPersons1" name="txtExtPersons1" class="form-fieldContractEntry"').attr({ type: 'text' });
$("#holder").append($ctrl);
}