I dont think they pay anything I the article itself it says it’s free to use and that the main factor to switch were the costs. In the comments there people also say that DHL doesn’t seem to donate to the project.

Here ist the part from the article translated to English:

Since there has been no announcement of the change from either Deutsche Post or DHL, the reasons for this step remain unclear. Presumably, cost reasons may have played a role. Deutsche Post had to pay fees to Google for the use of Google Maps. The data of Openstreetmap is under a free license and may be used without payment of license fees.