Safe to Delete Mobile Applications

Solution 1:

I would be careful. You may be backing up to iCloud, but syncing locally with iTunes. If you DO NOT sync your Apps with iTunes, you can throw it away.

Personally, I would keep it and maybe just delete some of the old apps you no longer use.

Solution 2:

Absolutely. If you aren't syncing apps from your Macbook to your iOS devices, it really isn't necessary for them to be there. And, if you ever need them on your Macbook again, you can always redownload them from iTunes (unless the app is removed from the App Store, which is rare).

Solution 3:

Hopefully this helps people in the future, it's ok to delete it locally from your Mac and it won't affect your iOS devices. Backup everything to iCloud and redownload from Apple Store. You can even do the same with iMovie and GarageBand (two apps I really don't use but take a bunch of space on my Mac Air 120GB).

Directly copied from iTunes below.

Are you sure you want to delete the selected apps from your iTunes library? These apps will not be deleted from any iOS device that synchronizes with your iTunes library.