If they use their original email invite link to reinstall credentials on their new device, the installation on the new device won't be successful. The credential is tied to the life of each device individually.
Touch io mobile credentials are only good for the life of the original mobile device. Once a new smart device is purchased, new credentials are required, even if the phone number and email have not changed.
To issue a credential to a new phone simply email another invitation to the user of the new phone.