When configuring, you indicate the identifier of the field in CF7 and the identifier of the 3rd-party field it maps to. The plugin will then take the submitted value from the CF7 form and map it to the 3rdparty field using the given name.
For example, pretending it uses GET method instead of POST, CF7 submits:
mywpsite.com/blah/?myemail=user526@email.com&myage=28&mycity=someplace,usa
You want it to submit to your 3rdparty like:
3rdparty.com/etc/?lead_email=user526@email.com&lead_age=28&lead_city=someplace,usa&someextrafield=arbitrary_value
Then you configure cf7-3rdparty like:
CF7 = 3rdparty
myemail = lead_email
myage = lead_age
mycity = lead_city
arbitrary_value = *someextrafield
where *someextrafield has the checkbox marked "is value" so it passes "arbitrary_value" instead of trying to get the value from CF7.
What behavior are you looking for? It sounds like you want the "arbitrary_value" scenario, which is also mentioned in #6 of the faq