iPad shows update available but iTunes says no

A few days ago, iTunes started reporting "there are no updates available for any of the apps in your iTunes library" whenever I click on the Check for Updates button. But iPad says there are updates. Something happened. Previously I've been using iTunes to update all apps, then sync to iPad.

Now, after something that happened but I don't know what, my iPad continues to find updates while iTunes continues to say "there are no updates available for any of the apps in your iTunes library." What settings control this?

Furthermore, when I update from iPad, each app after fully downloading and installing, remains there as a line item with the OPEN button instead of getting removed from the list. Is there a way to edit this growing list?