When you submit a web form and at the bottom of the page it says that it’s using re-captcha and the Google privacy policy and terms apply, what data is actually sent to Google?
Probably not a lot of data in itself but you’re definitely more fingerprintable given the captcha your machine did to validate it. 
Most of the time, if it’s an invisible captcha it’s just a matter of your input behavior: speed of typing, moving the mouse around the screen etc.
I can relate to your question: Question about 3rd Party Google Scripts