Looking for a simple tool to update a table

WordPress has an API available to allow external scripts to get data from your website and to add (POST) data to your website.
You can create a custom API endpoint where you receive the data from the other server and in a simple function create a new record in the WordPress database:

  1. Create a function in your functions.php to create a new record in the tablet.
  2. Add the new API endpoint in your functions.php

I know this is a very summarized explanation, but I hope this gets you in the right direction?