Are you just using the built in "Sharing" option in gnome settings for this?
If so install and run dconf-editor
there's a setting for "disable-background" which defaults to "off".
I've never tried changing this but it looks like it should do what you want.
EDIT: I believe there are settings in there that allow you to force encryption too, might be worth using if you're doing this over the internet without an ssh tunnel or vpn.
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