If the backup service is using file timestamps as the only key to refresh then it would have to store the last modification date and a good hash of each block, and when the date of the file being mirrored is updated scan each block to see if there is a change there and update the stored hash and timestamps accordingly. This would need to be orchestrated to reduce the risk of temporary corruption if there are several updates and the rechecking process coincides with a backup sweep (i.e. make sure you don't present updated dates for any block until you can present them for all needed).
For restoration, you either manually concatenate the parts or have an overlay filesystem that operates in reverse: showing the smaller block files as a single large unit.
You'd have to very thoroughly test the overlays and their interaction with the backup service before risking it on important data, so it might not be something you would genuinely consider...