Is it obligatory to seek out and obtain absolution from those to whom the network belonged, or is giving charity on their behalf, equivalent to the value of the used subscription, sufficient?

It is not permissible to benefit from private networks belonging to their owners without their permission. The fact that they are unprotected does not make their use permissible, for the Prophet, peace and blessings be upon him, said: "The property of a Muslim person is not lawful without his willing consent."

If leaving the network unprotected is not considered customary permission, then you must compensate the owner for the benefits he missed out on. If you are unable to seek his forgiveness, then give in charity an amount equivalent to the benefit you encroached upon. If you know the owner of the network and informing him would cause embarrassment, then deliver the money to him without informing him.

However, if leaving the network unprotected is considered customary permission, then there is no blame upon you for connecting to it, and no compensation is due from you; because customary permission is treated the same as verbal permission.