Thanks for the hints.
Unfortunately I wasn’t able to apply any changes to the files copied into my child theme. I have tried to copy it into various folder settings but nothing allowed me to make any changes visible in the cart.
My php knowledge is perhaps a bit better than beginner but I would have to sit ages to find out the right code.
I will leave it as is for now but maybe you could consider to add this feature to a future update?
Also it would be great if in the cart in the price column the actual price of the product would be shown instead of Free! so that the user would know the actual value of the free product that she will get.