Removing a drive from Mac “correctly” is necessary to avoid damage to your Mac and the drive. If you have been receiving messages like “Disk Not Ejected Properly” on your Mac, then probably you have not been ejecting the drive correctly.
Not ejecting the drive or any other USB can also result in data loss and can tamper with your Mac or drive. In order to avoid the message popping up the next time you insert the drive, here's what you should do:
How to Remove A Drive from Mac to Avoid “Disk Not Ejected Properly” Alert in Mac OS X
Step 1: Open the Finder.
Step 2: In the sidebar of the Finder window, there will be a sub-menu titled “Devices.” You can find your disk under this sub-menu.
Step 3: Next to the disk name, there will be an eject icon. Click on it and wait for a few seconds till the disk completes ejecting. You can then remove the drive.
Step 4: Alternatively, you can also eject the disk by selecting it within the Finder's File menu and then selecting, “Eject XXXX” (XXXX being the name of the drive.)
Other than these steps, you can always return to old methods such as dragging the drive icons to trash or by using the keyboard shortcut for ejecting a drive.
Note: Even after following these steps, if you see the error message again, it can be because you ejected the disk while it was in operation, i.e, if the disk was taking a back up or was copying something. In that case, wait till the process is complete or quit the application. Note that even after clicking the eject icon, you might have to wait a little while before it's safe to remove the disk.