Is Four Square giving back to OpenStreetMap?

Why are there stores on Four Square that aren’t on OpenStreetMap? If Four Square is using OpenStreetMap shouldn’t their additions be on OpenStreetMap?

For example Deb’s Convenience Mart on Salina Street in Syarcuse is not on OpenStreetMap but it is on Four Square

Good question and one that deserves attention. Particularly if the rumours are true that Foursquare is talking with Apple Maps about data sharing. As they are using OSM themselves, it would not be particularly fair if they only allowed our competitors to use their data.

See this article about MapBox and FourSquare helping to improve OSM:

No, they haven’t released any of the data for places yet. And it is not required for them to do so. You can use non-free data as an overlay on OSM maps if you want.
And any sort of bulk import from FourSquare to OSM would probably be a bad idea.

So because they are using an overlay it doesn’t count as a derived work?

Overlays have always been treated by the OSM community as a collective work, not a derived one, if the information was produced without reference to OSM data.