I would use AJAX, and specifically I would use jQuery to make AJAX simpler. You don't have to use jQuery though. The strategy is:
- Give the <td> you want to update a unique ID.
- Respond to a click event on a button labeled "Update". Respond to this event with jQuery.
- Use jQuery to call the php script on the remote server.
- Using jQuery, update the HTML of the <td> using the ID you created in step 1.
Using
load() in the first example in this tutorial is probably a good place to start:
5 ways to make AJAX calls with jQuery