License question: Save attribution with copied data?

I have a question about attribution requirements. If I access OpenStreetMap data and save the OSM data into a database, do I need to save an attribution with the saved data? Do I then need to display that attribution every time the saved data is accessed?

Here's what I want to do: I'd like to create a "driving distance calculator" for a database application. My software will run within a database application. My software will take two addresses from the database, geocode both of them, then calculate the driving distance between them (using a routing service). Once the driving distance is possessed, my software will save it into the database.

This will run on the "view page" of a single record. The user will have a single record open, and on the view form they will see a "Calculate Driving Distance" button. Clicking the button will invoke my software as described above. I plan to add the required attributions on this page, for both the OpenStreetMap data and the MapQuest API.

But after that has occurred and the data is now saved in the database application, do I need to maintain an attribution with the saved copy of the data? I want to write my software so that it can use different mapping services, so it's possible that the driving distances saved on different records were acquired from different mapping services.

The saved driving distance will be used for private purposes only, and won't be republished. The database application is a password-protected application. My software may be used by both commercial and non-profit organizations.

Thanks! - Nathan