Hi mdesignffm,
It sounds like you are on the right track. After deleting the apps from iTunes, use the “Transfer Purchases” feature to transfer the apps from your iPhone to iTunes:
Re-download or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - Apple Support
http://support.apple.com/en-us/HT201267
Transfer your purchases to your computer
Before you transfer your purchases, make sure that your computer is authorized with the same Apple ID account you used to make the purchases. Learn how to authorize your computer using iTunes.
If you bought the iTunes Store content on your device using multiple Apple ID accounts, you'll need to authorize the computer for each one.
To transfer purchases from your device to a computer:
Connect your device to the computer. Wait for its icon to appear in iTunes.
Go to File > Devices. If you're using iTunes for Windows and can't see the menu bar, learn how to turn on iTunes menus in Windows.
Choose Transfer Purchases from [device name].
This feature works only for content bought from the iTunes Store. Any items that you imported from audio CDs or received from other sources won't copy from your device to the iTunes library. However, all podcasts from your device's Podcasts app and copies of all PDFs and books from your device's iBooks app will transfer to the computer. Learn how to transfer media to your iTunes library.
- Matt M.