Sorry folks – I misread the original posting and thought the dog door had been installed by a previous owner (too much festive spirit, I fear).
If the current owner installed the dog door then they have to pay for the repair of the window, in my view, as it was damaged by them in the first place and arguably weakened by the installation, not to mention what happened during the burglary. No dog door, no burglary, no breakage would be my logic and this would come under damage to common property.
My view is similar to but probably a little more aggressive that Whale’s. Charge them for the repair and then tell them if they want a dog door it will require a by-law that transfers ongoing maintenance of the door to the current and subsequent owners. No by-law, no dog door – simple as that. If they baulk at that, comprise if you want to on how much they pay but make sure you establish that they were in the wrong to fit the dog door without permission.