yes, it could be worth the case to add some line in the vCenter Migration Tool Documentation.
This behaviour is not immediately evident if the jobs have enabled the "failover to standar backup", because backups still work, but loose the advantages of storage integration.
Luckily i like to double check things
As mentioned before, performing a clone of the job, deleting the old one and mapping new job to the old files is fast to be done, and ensure that new job has exactly the same setting of the former one.
P.S.: It's also a good idea to try a restore, after all this work