Store URLs in WebappDataStorage, and purge them when history is cleared.

chrome/browser/android/webapps/webapp_registry.h

Index: chrome/browser/android/webapps/webapp_registry.h
diff --git a/chrome/browser/android/webapps/webapp_registry.h b/chrome/browser/android/webapps/webapp_registry.h
index 26357bcd56edc2ad0833aadeb2398228e22a83b4..37975598ed30518cd2bae36a20e0566e96874df0 100644
--- a/chrome/browser/android/webapps/webapp_registry.h
+++ b/chrome/browser/android/webapps/webapp_registry.h
@@ -20,6 +20,10 @@ class WebappRegistry {
   // Cleans up data stored by web apps.
   static void UnregisterWebapps(const base::Closure& callback);
 
+  // Removes history data (last used time and URLs) stored by web apps, whilst
+  // leaving other data intact.
+  static void ClearWebappHistory(const base::Closure& callback);
+
  private:
   ~WebappRegistry() = delete;