How do I add or remove reward points for one customer?

A customer's points are managed on their own profile, not on the plugin page. Go to Customers → Manage Customers, open the customer, and click the Reward Points tab.

There you can see their balance and history, and enter a manual adjustment, then click Apply.

Plugins → Reward Points only holds the store-wide earning and redeeming rules. The plugin comes with your plan or can be added from the Plugins page.