Is it permissible to cash a check for 40 Euros obtained from a European company that provides a service of compensation for purchases made from websites, knowing that the check was granted for purchasing an inexpensive item during a free trial period, with the prior intention of not subscribing to the service, and is subscribing to such services permissible in Sharia?

The aforementioned transaction is impermissible due to the presence of gharar (excessive uncertainty) and jahalah (ignorance concerning the subject matter). Your registration for the free trial period with the intention of not subscribing, in order to obtain the check, is not permissible. It involves consuming wealth unlawfully. You must repent and disburse the amount of the check to charitable causes or to the poor and needy.