I just tried this and it worked for me:
1. In a separate tab enter one of the following URLs
---www.arcgis.com/sharing/rest/content/items/<itemid>/data?f=pjson
---<orgkey>.maps.arcgis.com/sharing/rest/content/items/<itemid>/data?f=pjson
Change the <itemid> and/or <orgkey> for the Web Map id
2. Open the details of your web mapping application and click edit.
3. At the bottom change the purpose to Configurable.
4. Copy the json text from step 1 and paste it in the Configuration Parameters section at the bottom.
5. Edit out the empty json tag that is in the basemap gallery section that looks like {},
6. Save and refresh and that should do it.