When someone visits a page on your site, Independent Analytics makes a single REST-API request that records the visit. Without the ability to use the REST-API, it cannot record any data.
At the same time, you may be aware of the security concerns raised by the REST API. While it doesn’t directly create vulnerabilities, it does expose information that could be used in conjunction with another attack.
The good news is that you can selectively disable REST API routes without deactivating the API entirely. This is made possible via the excellent Disable REST API plugin.

Once you activate the Disable REST API plugin, you’ll find a new menu at Settings > Disable REST API. In this menu, you can click on the /iawp route to enable it, and then save your changes.

This will ensure that the /iawp route can be triggered by your visitors while locking down all other routes.
If any of your other plugins depend on the REST API, make sure to enable their routes too.