Your new maps need to have an on-map credit to OpenStreetMap, as that's where the map data comes from, and OSM's licence requires attribution. osm.org/copyright explains how.
That's not on-map, that's hidden behind a click. osm.org/copyright makes it very clear that the attribution needs to be on-map. You don't see Google permitting people to hide their brand away like that!
Apple's maps are not just OpenStreetMap - there's a lot of other data sources in it too.
For the OSM data Apple do use, I think it's quite old OSM data from 2010-2011 or something. As far as I remember, they used that because the license changed after that, so I believe that's under different terms.
Doctor_Fegg makes a good point. The OSM Legal FAQ states: "For a browsable electronic map (e.g. embedded in a web page or mobile phone application), the credit should appear in the corner of the map, as commonly seen with map APIs/libraries such as Google Maps." Link: http://wiki.openstreetmap.org/wiki/Legal_FAQ#3a._I_would_lik...
Your new maps need to have an on-map credit to OpenStreetMap, as that's where the map data comes from, and OSM's licence requires attribution. osm.org/copyright explains how.