Sparse Bundle Time Machine backup turned into package file with blank icon

Would help if you could tell us what operating system that you are running on your MacBook, since Apple made a number of changes regarding Time Machine with the introduction of the Catalina operating system, which has caused a number of issues for users.

For example, Catalina Time Machine backups are no longer stored within a sparsebundle, they are instead stored in a file that Apple calls a backupbundle, whatever that might be.

Unfortunately, Apple has not documented any of the changes, so there is not much to go on at this point as far as troubleshooting issues.

So, the first thing to understand here is whether you have "upgraded" to Catalina and whether your wife has done the same on her MacBook. (She probably has not, according to the info in your post).

After you "upgraded", the first Catalina Time Machine backup is supposed to go through a change from a sparsebundle file to a backupbundle on the Time Capsule hard drive. A number of users.....like me..... are finding out that this does not always occur.

I don't know why. Another user might be able to help.

If you don't see a ".backupbundle" after the name of your Mac when you use the Finder to look at the Time Capsule hard drive, something went wrong. The backupbundle should have an icon that looks like this:

Unfortunately, as we mentioned above, Apple has provided no troubleshooting documentation for Time Machine with Catalina.

If you want to try to go further with this, my advice would be to make complete backup copy of the file that exists on the Time Capsule on another USB drive......to try to preserve the backup data that might be contained within the file. Then, we can try to change the file name back to .sparsebundle to see if that helps.

Other users have reported that the file change has occurred OK, but they are not able to view any of the old backups that were made prior to the upgrade to Catalina. This may occur for you as well.

If you are not concerned about the old backups, my suggestion would be to trash the file that exists on the Time Capsule and then try to start over again with a new backup with the Catalina Mac.

In addition, I would recommend that you add another backup plan using reliable software like Carbon Copy Cloner, since Time Machine is proving to be less than reliable.

Change the name back to sparsebundle seems to be fixing it for lots of people.

DO note.. it might be worth moving to a 3rd party backup software now.