What is the ruling on using other people's internet without their permission, and is the one who does so considered a thief, and how can one atone for this while preserving one's reputation?

If you are unable to seek forgiveness from the owners of the networks whose network you used without their permission, you must return the value of what was used. If you do not know the exact amount, then determine the amount that you most likely believe fulfills the right or exceeds it. It is not a condition to inform them that you used their network without their permission; it is sufficient to return the right by any means that does not result in harm or embarrassment. As for those whom you cannot reach, give charity on their behalf equivalent to the value of their right.