Security deposit and damage liability

A friend of mine recently moved out of a rented apartment and didn’t report some water damage on the wooden area around the cooktop, which developed blackish stains and discoloration. 🤷‍♀️

My friend admitted the damage was his fault at that point.

Now the landlord wants to repair the damage and provided a repair estimate from a company of about 700€, to be withheld from the security deposit.

He also said he will share the final invoice once the work is completed as proof that the repair was actually done.

Is there any hope to contest this, possibly without taking it to court?