PS Can you please explain why they appear in the first place - and whether there's anything we can do prevent them appearing?

As I said earlier: They can be added manually by accessing the dialog you initially displayed.
They can be added using macros.

SharePoint is one of the programs that create document properties here and can also place them in the Quick Parts > Document Properties
XML location of Document Properties in Quick Parts list - Expand / Modify

Other than make the documents Read-Only, there is nothing you can do to prevent others from adding them.
You can ask them to not add them. You can remove them when the documents come back to you. Unless your correspondents are very technically inclined, these are not something that is going to bother them. Again, most users never see Document Properties.