Can't Repair Disk Error Message After Using Passport on Second Computer

I have been using My Passport for Mac to back up an old MacBook Pro that runs on 10.10.2. I also was dragging songs from iTunes to the Passport for backing up. I recently bought a brand new MacBook Pro (running on Catalina) and used My Passport to move all my backed up mp3s to the new computer. That may have been a mistake - when I next connected My Passport to the old Mac I got the error message “OS X can’t repair the disk…You can still open or copy files on the disk. Back up the disk and reformat it as soon as possible.” I reformatted the Passport and backed up the old Mac again, and as an experiment, I then connected it to the new computer, moved a few mp3s onto it, and got the same error message when I reconnected the Passport to the old Mac.

I thought you could use the Passport on multiple computers but is the OS difference an issue?

Any advice or tips appreciated. Thank you.