reCaptcha on the register #modalIR

I have searched the forums regarding this and many want to redirect to a different page. However, I just wanted to add the reCaptcha onto the #modalIR popup when a new user registers. The reCaptcha plugin I downloaded adds the reCaptcha to the default login page here https://frsquad.com/wp-login.php?action=register . The only way users can get to this part is going to ‘login’ #modalIL then ‘sign up’ link. My issue or possible concern is bot registration. If bots don’t use the ‘register’ link in the top right, then I don’t need the reCaptcha there I suppose but I am not 100% sure if spam bots use this link. From what I have read they scrape for the domain/wp-login.php?action=register link. If this is the case, then I may not need reCaptcha on the #modalIR popup screen.

I have the code ready to add the reCaptcha to the #modalIR window. Just not sure where to put it as google tells me to put it in a <form> tag area or something.