How can I access the Header of and ajax response from the rest API

You can use change ajax this: request.getResponseHeader('your_header')

$.ajax({
    type: 'POST',
    url:'api-url.php',
    data: formData,
    success: function(data, textStatus, request){
        alert(request.getResponseHeader('your_header'));
    },
    error: function (request, textStatus, errorThrown) {
        alert(request.getResponseHeader('your_header'));
    }
});