It is important to know that without additional setup in GTM you will not see any data about form submissions in GA.
My plugin generates a so called data layer event upon every form submission with the event name gtm4wp.contactForm7Submitted
You will need to setup a trigger in GTM that fires on that event.
Next you will need to setup a GA tag by setting either a GA event or a virtual pageview. This new tag should fire using the trigger created in the prior step.
I hope that help you getting the right data into GA.