i opened the ebay apk, and the AndroidManifest.xml file in it.
i'll go out on a limb and say that since all its activities have this:
android:excludeFromRecents="true"
it's why we don't see them in the recents.
as stated:
android:excludeFromRecents
Whether or not the task initiated by this activity should be excluded from the list of recently
used applications, the overview screen. That is, when this activity is the root activity of a
new task, this attribute determines whether the task should not appear in the list of recent apps.
Set "true" if the task should be excluded from the list; set "false" if it should be included.
The default value is "false".
