I have a "Remove" button next to app icon on iTunes' app-page
Are you referring to the App section of the iPad that you are viewing on iTunes?



If so, the Remove button removes just removes the app from the iPad. It only permanently deletes the app from the iPad. You don't have to worry about it being deleted from iTunes or even from your Apple ID. To re-install the app from to your iPad, you will just need to click on "Install" (it will replace the "Remove" button) or go to the App Store, tap Purchases, and find the app, then tap on the icon with the cloud and a down arrow.