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 despite the fact that 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.
The T&C are best checked before booking the car. Should you use the German version of the check24 web page, click on "Details und Mietbedingungen" (Details & T&C) below the offer and then click on "Mietbedingungen". I just checked a random offer, where the following is written about taking the car abroad:
Westeuropa: Fahrten sind in alle westeuropäischen Länder erlaubt. Alle
bereisten Länder müssen zum Buchungszeitpunkt angegeben und auf dem
Voucher vermerkt werden
Translated to English this means:
Western Europe: Journey to all western European countries are permitted. All countries travelled through (and within) must be listed at the time of booking and must be listed on the rental car voucher.
So for this offer, you can only take your car abroad to the Netherlands if you notify the rental car company at the time of booking. This could be the case for your offer as well.