This is the plugin “Quick Icon - Akeeba Backup Notification” which you can either configure or disable.
The option “Stale backup time, in hours” controls after how many hours since the last backup the icon will tell you the backup is out of date. If you want it to be, say, one week you can set it to 7 days times 24 hours in a day = 168. If you want to disable the warning altogether just set “Enable warning icon” to No. This will still show you the backup icon which, when clicked, takes a backup with the backup profile specified in the “Backup Profile” option.
If you do not want to see this icon at all, unpublish the plugin.
Nicholas K. Dionysopoulos
Lead Developer and Director
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