This turned out to be a nice challenge. Try,

$ sudo mv /usr/bin/gsettings /usr/bin/gsettings2

$ sudo gedit /usr/bin/gsettings

$ sudo chmod +x /usr/bin/gsettings

When gedit comes up on the second instruction, add:

#!/bin/bash

if [ "$1" == "set" ] && [ "$2" == "org.gnome.desktop.background" ] && [ "$3" == "picture-uri" ]; then

    a=$(zenity --entry="Password")

    h1=$(/bin/echo $a | /usr/bin/md5sum | /bin/cut -f1 -d" ")

    h2='a799d7cf3d9ca647f1320fc6bfaf7408' #Password hash

    if [ "$h1" == "$h2" ]; then

    gsettings2 set org.gnome.desktop.background picture-uri $4

    else

        zenity --notification --text="Wrong password. Come again another day"

    fi

else

    $(gsettings2 $@)

fi

To undo,

$ sudo rm /usr/bin/gsettings

$ sudo mv /usr/bin/gsettings2 /usr/bin/gsettings

You can go to this md5 generator, put your string and replace a799d7cf3d9ca647f1320fc6bfaf7408 with whatever you like. Try finding out for yourself what this corresponds. You'll realize how secure this is.

Even if somebody views this file, without your password they cannot change it (This is similar to how linux stores your passwords :P).