You will not be stopped at the border and most likely your rental car company will not get to know that you crossed the border -- that is, unless you will be involved in a car accident or get a speeding (or parking) ticket.
All rental contracts are different, however, and hence you really need to look it up in the terms and condition of your rental contract. Check24 only acts as a search engine, though, and even if their interface suggests otherwise, your rental contract will be with another company.
Note that insurance is often split if you book a cheap fare with a full-service insurance package - the car rental company (e.g., Avis) will provide the basic insurance, and the collision damage waiver will be provided by a different insurance company - in this case you will need to read two sets of terms & conditions.