Skipper escaped into a badger sett in November 2012 after he was taken for a walk by one of Almut's friends in the Tegel area of north Berlin, the Berliner Morgenpost reported.
It took 40 firemen eight hours to dig several metres into the ground and find the missing dog.
Although the fire service warned that Almut would have to bear the costs of the rescue, she argued in court that the €13,000 bill they first sent was to much for the work.
She also said that she should not have to pay the full amount as it was her friend's fault, rather than her own, that Skipper got lost in the first place.
But she agreed to pay the lower amount of €10,000 after the judges warned that they would reach their own decision if she could not agree with the firemen.