The tampering or corruption error means that at some point the checksum value when loading a save did not match the value created when the save was made. This means either something became corrupt or there was a problem with the loading process, but there is no way to tell just from that if that will cause a problem or how serious it may be. Once this check fails a flag is set in the save, so any saves made after that point will always give this warning.
If you did not resave after getting the warning, try clearing the Xbox cache, to see if that will help (it may if there was a problem loading the save).
- press and hold the Xbox button on the front of the console for 10 seconds until it shuts down
- unplug the power cable and wait 30 seconds
- plug the console back in and turn it on
- log into the same Xbox Live account you were using, start the game and let it sync, if required
Do you have access to a different Xbox, where you can log in to your account and try downloading the cloud copy of the save? If that works (the problem happened after the save was made and synced), you could delete the local copy of the save on your Xbox, and get it to sync. If the problem happened during the save process or before Xbox Live synced, this would not help. Note that if you have other playthroughs going, there is no way to just delete individual local files on Xbox.
Unfortunately, the checksum value is calculated across all of the save data, so there is no way to identify what changed (if anything), and there is no way to get a save off an Xbox to be able to check it. For what it is worth, I've checked a handful of PC saves in the developer build of the game that gave this error, but loaded properly, and none triggered any critical errors or errors that indicated corruption; some were honour mode saves, or otherwise didn't have any recent saves the players were able or willing to revert back to, and I have not seen any subsequent reports of issues later in the game from continuing.