Deleting mobile applications from Mac/iTunes 12.5
If you sync a device with the computer, and the apps don't already exist on that computer, they will be transferred from the device onto the computer. (This may only apply to apps newly downloaded since your last sync.)

If you're using iTunes 12.5.1, it's now accessible through the drop-down menu that allows you to switch between Music, Movies, Podcasts, etc., as Apps. If it's not visible on that menu, choose the Edit Menu item on the menu and check the box next to Apps, hit Done, and then click on Apps.

Once in Apps, you can remove them by right-clicking on an application (or selecting several and then right-clicking) and choosing Delete, then Delete Apps, then Move to Trash.

You can set your computer to automatically download new apps that you purchase on your device under Preferences > Store tab > Automatic Downloads and check the box for Apps.

If you restore a backup from iTunes, it does the restore and then does a separate sync step where it loads the apps back onto the device. I don't know what would happen if the apps weren't on the computer to be put back on, though. If you restore from an iCloud backup, the apps are re-downloaded over the internet.