In order to find the production of entropy on a process between a system and a reservoir, it's useful to consider that reservoir passes through a reversible process. Why is that?
The definition I have for reversible process is that it is a process that can be reversed without leaving marks on the surroundings.
So, if I transfer heat from my system to the reservoir, its temperature wouldn't change. Also, if the reverse happened it wouldn't change the temperature either.. so it could be approximated to a reversible process.