I would simply import them from the Kindle into calibre, no need to redownload.
Deleting them from the Kindle before resending is advised if the filename will change, or if you are sending a legacy mobi7 book -- the Content Catalog can get confused about what books you have, and esp. play havoc with collections.
a/k/a sez Kindle: Why the #$%^& are there two different books with the same unique ID?
As long as a book was not converted, it retains the exth 113 (ASIN) field which the Kindle uses to manage collections.
calibre cannot modify the metadata on a dual-MOBI -- but I doubt that's what Amazon is sending you!

Sorry, all my books get sent with the title properly fixed.
Note: DeDRM is not required, calibre can track and change the metadata on a DRMed book. However, DeDRM doesn't actually cost anything.