A backup of a server from which Exchange has been removed fails with the error "The Exchange integrity check utility failed to load".
When Exchange is uninstalled, the value for the registry key
is removed, but the key itself is not. During a backup, ESE detects that Exchange is present on the server (even though it is not) and attempts to load the relevant libraries to run an Integrity Check. Since no libraries exist, this attempt fails, causing the backup to fail.
Remove the ExchangeInstallPath key from the registry altogether (right-click > Delete) and run the backup again.