I have already tested this module in 3.1. In the download link page we have separate zip file for 3.1.
Please let me know if you have any issue.
Thanks for your review.
We have made few tests on Joomla 1.7 and all works fine. Joo ReCaptcha 1.6.x is 100% compatible with Joomla 1.7
If you find any issue please open a topic on our support forum ( http://joomla.stefysoft.com/forum/ )