Gross negligence is committed by a person who "grossly disregards the care required in traffic, who fails to observe what should be obvious to everyone under the given circumstances" (established case law since RG [Reichsgericht, supreme court of the Reich] vol. 141, 131).
This refers to actions that a prudent person would not do, for example driving under the influence of drugs or alcohol, driving through a red light or adjusting the car seat while driving.
In the case of rental cars, there are other negligent behaviours, for example a lost rental car key, disregarding the rental conditions or not filing the police report. Damage caused by negligent actions will not be reimbursed by the rental car providers.