Hi > lawyerlinguist Can you confirm that?
Joomla reCaptcha plugin is a joomla core component and it is showed when set from global configurations in all Joomla contacts forms
If you are using an external contact form you will need to verify that this contact form allows to use Joomla reCaptcha plugin
For example indeed some other forms uses own reCaptcha plugin like RSForms Pro
So if we do not know which specific form are you using we cannot answer at all at your question , that's why we asked to have a look at it before.