Using the command efibootmgr -v I could see that the entry named ubuntu points to the Ubuntu 17.10 EFI disk and the one named linuxmint points to a non-existent disk. From this article I learned that "Linux Mint uses an EFI boot directory named ubuntu, which obviously conflicts with what Ubuntu itself uses". So the entry named linuxmint was a red herring, both Ubuntu and Linux Mint use the entry named ubuntu, and since this list is stored in the computer itself, Ubuntu overwrote the entry for Linux Mint, even though the Linux Mint boot drive was removed during install.