A small extension to the reCaptcha library
The $error field should be private (Why use getters and setters?). Currently users of the Captcha class can modify the value of the $error field directly which. It's not a good idea to allow them to do this.
What's the point of returning with false in the check function when the response is not valid while if it's valid the function does not return with true?
The render and check functions seems somehow temporarily coupled. See: Clean Code (by Robert C. Martin), G31: Hidden Temporal Couplings

References:


Effective Java Second Edition, Item 38: Check parameters for validity (I know that this is a Java book but this chapter applicable to PHP too.)
Function/method argument validation standards