How do you update a django template context variable after an AJAX call?

you cannot this way. Better way would be to load that part of your html via ajax.

your ajax view:

def update_items(request):
    product_list = your_data
    return render(request, 'table_body.html', {'product_list':product_list})

your main html:

<tbody class="table_body">
   {% include 'table_body.html' %}
</tbody>

table_body.html:

{% for item in product_list %}
  <tr>
     <td colspan="2">{{ item.date }}</td>
     <td id="item_name_format" colspan="6">{{ item.name }}</td>
     {% if item.category_id %}
      <td id="item_name_format" colspan="2">{{ item.category_id.level1_desc }}</td>
     {% endif %}
      <td id="item_amt_format" colspan="2">${{ item.amount|intcomma }}</td>
  </tr>
{% endfor %}

your ajax would look like this:

function update_item(item_num) {
    console.log(item_num) // sanity check
    $('.table_body').html('').load(
        "{% url 'update_items' %}?item_num=" + item_num
    ); // <--- this code instead of $.ajax(lala)

you use this load() here