Recovering song list from deleted device

Moderator edit: moved to iOS thread

Looks like my kids deleted iRealPro from my iPad. I have it on my phone, with a somewhat (less than a year old) recent copy of the iPad songs, but I was wondering if I can get a more recent file from my iMac with Time Machine or something. I sync the iPad to the iMac pretty regularly, and thought it was making backups every time but apparently not. The only backups are the one's I have deliberately made.

Any good way to recover that list? Does it even exist on the iMac after sync?

We're not aware of any tools to extract a specific information from an iOS backup.
One way is to restore the backup of your iPad. Here are the steps:
https://support.apple.com/en-us/HT204184