Apple - How can I disable the "no backup in x days" from TimeMachine?

When you don't have the external hard drive hooked up, go System Preferences >> Time Machine, and switch it to OFF. You will still be able to perform backups, it just won't happen automatically.

In newer OS versions, you must uncheck the Back up automatically box and then right-click on the backup disk on the right side and select Stop using ‘Time Machine’ Backups.

This is the technique that I use, and I don't see notifications.

As mentioned previously, the process to disable these notifications has slightly changed as of High Sierra.

I'm on 10.13.2 and here's the process that I followed:

• After unchecking Back Up Automatically in the System Preferences > Time Machine section, I was still receiving the messages.
• I also went ahead and removed my old backup device from Select Backup Disk... and then the warnings have stopped coming up (fingers crossed).