Connecting to the Internet whether fixed line or mobile has a number of hidden pitfalls. Leaving it permanently connected and using up your sometimes precious allowance of data in tasks you did not know about is one of them.
This was the case with one post that I came across where a good well intentioned son had purchased a data bundle from one of the cell providers to allow him access to mail.
He found his data consumed and far more than sending and receiving an email would do. He found that Windows was turning on updates again as it does. Others commented on this and he corrected the problem but I had an additional suggestion or 3.

Windows updates and do you do them automatically, manually or not at all is a good debate. What I did with my father who is very advanced in years was to disable all updates completely. He brings his laptop round every 3 months or so and I connect it to my LAN and BroadBand connectivity and do the updates that way. I do the same with his anti virus as well.
It might be sensible as well with those of advancing years to remind them that in their youth they would not have left the phone off the hook or they were charged for the call. So it might be an idea to unplug the modem after accessing mail.

Anywho that is my suggestion