To switch off automatic upgrade checks in SyncBack, select Global Settings from the burger menu, then untick the checkbox Check periodically for new versions. The burger menu is the three horizontal lines at the top-left corner of the window: 

If you are using a retired version of SyncBackPro/SE then you may wish to switch off automatic upgrade 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 now longer available for them. Visit our upgrade store if you wish to upgrade to the latest version.