From plugin 24.7, every new saved reply will belong to a user. This is different from before where all saved replies didn't belong to anyone and was available clinic wide.
When creating a new saved reply, you will have presented with an option to make it clinic wide to preserve that feature.
For existing saved replies, the first user to edit it will claim ownership of the saved reply. From then on, only the owner has the access to edit them.
We recommend users to have 1-2 users that create responses clinic wide, and individual users to have their own set of private ones that is used day to day.