Missing iPhone Apps

Hello,

I have a number of iPhone apps which are on my iPhone, but are not on my computer. In iTunes, in the Apps section of the Library, I can see all of my apps, but the ones that are not on my computer have a missing icon with a small exclamation point next to their names. If I double-click on these or select "Get Info," I see a dialog stating that it's missing --

The app "Remote" could not be used because the original file could not be found. Would you like to locate it?

My question: How can I transfer these apps from the iPhone to my computer, so that they show up properly in iTunes?

A few notes:

1. The apps really aren't on my computer. They really aren't.

2. I have sync'd, and performed a backup. I have also performed a full reset of the iPhone, with a subsequent restore and a re-sync.

3. The apps are on my phone. I can delete them and then re-download them via the iPhone's Apple store interface without any problem.

4. I am unable to download them using iTunes store, as the link to purchase and download is labeled "Downloaded" and is greyed out. There is no apparent way to re-download any of these problematic apps via the iTunes interface.

5. I have only one iTunes Library. I do not back up to iCloud. I use a USB cord for my syncs and backups.

Many thanks in advance!