No, there is (or was) just Google Captcha. Here is issue on Github about it.

https://github.com/signalapp/Signal-Desktop/issues/6002

It's possible but if there's no transparency you can also assume the worst

Is that something that can be done?

Unless I'm mistaken, they use services provided by third parties, perhaps PayPal as indicated in the source code. But guess what - there's no mention of PayPal in privacy either.