To switch off automatic update checks in SyncBack V9 and newer: select Global Settings from the burger menu, then untick the checkbox Check periodically for new versions. The checkbox may be disabled, in which case update checks will not be made as the version you are using knows it is no longer being updated. The burger menu is the three horizontal lines at the top-left corner of the window: 
If you are using SyncBack V8 or older: select Preferences -> Options from the main menu, and untick the checkbox Check periodically for new versions on the Easy settings tab. The checkbox may be disabled, in which case update checks will not be made as the version you are using knows it is no longer being updated.
If you are using a retired version of SyncBackPro/SE then you may wish to switch off automatic update checks as no new releases of those versions will be made. You are free to continue using retired versions, but note that technical support is no longer available for them. Visit our upgrade store if you wish to upgrade to the latest version.