What is the ruling on using a mobile application that provides internet service with a very small annual subscription, without paying fees to the telecommunications company that owns the transmission towers? Does the company have a right over the user? And what should the user do with the materials (lessons, books, programs, summaries) downloaded from this application if its use is impermissible?

The ruling on your action depends on knowing the extent to which the telecommunications company permits the capture of its network and the use of the application.

If what you did was an infringement on its right, then you must pay the value of the benefits you caused its network to miss out on, to be estimated by experts. If it is impossible to pay it to the company, then give it as charity on behalf of its owners.

However, if that was permissible, then nothing is required of you.