Igen, használom a Grub Customizert.

Egy kis pontosbítás. Most vettem észre, hogy az MX Linux /etc/default könyvtárában nincs ez a grub.ucf-dist file.
De a Linux Mint /etc/default könyvtárában viszont megvan.
A boot folyamat az MX Linux grub-ját használhatja, mert ha abban módosítottam pl. a várakozási időt a Grub Customizerrel, 
az rögtön érvénybe lépett a következő rendszerindításkor,. Továbbá  a korábban telepített Mint esetén a grubnak nem volt "képes" háttere,
az MX linux grub már háttérképpel indul, ezt látom induláskor. Szóval ebből gondoltam, hogy az MX grub az "aktív". 

Mindkét Linuxba telepítettem az apt-file alaklamzást. 
Rákerestettem a apt-file search grub.ucf-dist paranccsal, de a grub.ucf-dist fájlt egyikben sem találta meg.

Az UCF telepítve van, ezt írta ki a terminál:
courage@OptiPlex-9020:~$ apt-cache policy ucf
ucf:
  Telepítve: 3.0043
  Jelölt:    3.0043
  Verziótáblázat:
 *** 3.0043 500
        500 http://archive.ubuntu.com/ubuntu jammy/main amd64 Packages
        500 http://archive.ubuntu.com/ubuntu jammy/main i386 Packages
        100 /var/lib/dpkg/status

Végül a grub fájlok tartalma:

A Linux Mint-ben /etc/default/grub

# If you change this file, run 'update-grub' afterwards to update
# /boot/grub/grub.cfg.
# For full documentation of the options in this file, see:
#   info -f grub -n 'Simple configuration'

GRUB_DEFAULT="0"
GRUB_TIMEOUT_STYLE="hidden"
GRUB_TIMEOUT="30"
GRUB_DISTRIBUTOR="`lsb_release -i -s 2> /dev/null || echo Debian`"
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash apm=power-off"
GRUB_CMDLINE_LINUX=""

# Uncomment to enable BadRAM filtering, modify to suit your needs
# This works with Linux (no patch required) and with any kernel that obtains
# the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...)
#GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"

# Uncomment to disable graphical terminal (grub-pc only)
#GRUB_TERMINAL="console"

# The resolution used on graphical terminal
# note that you can use only modes which your graphic card supports via VBE
# you can see them in real GRUB with the command `vbeinfo'
#GRUB_GFXMODE="1024x768x16"

# Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux
#GRUB_DISABLE_LINUX_UUID="true"

# Uncomment to disable generation of recovery mode menu entries
#GRUB_DISABLE_RECOVERY="true"

# Uncomment to get a beep at grub start
#GRUB_INIT_TUNE="480 440 1"


A Linux Mint-ben /etc/default/grub.ucf-dist

# If you change this file, run 'update-grub' afterwards to update
# /boot/grub/grub.cfg.
# For full documentation of the options in this file, see:
#   info -f grub -n 'Simple configuration'

GRUB_DEFAULT=0
GRUB_TIMEOUT_STYLE=hidden
GRUB_TIMEOUT=10
GRUB_DISTRIBUTOR=`lsb_release -i -s 2> /dev/null || echo Debian`
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash apm=power-off"
GRUB_CMDLINE_LINUX=""

# Uncomment to enable BadRAM filtering, modify to suit your needs
# This works with Linux (no patch required) and with any kernel that obtains
# the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...)
#GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"

# Uncomment to disable graphical terminal (grub-pc only)
#GRUB_TERMINAL=console

# The resolution used on graphical terminal
# note that you can use only modes which your graphic card supports via VBE
# you can see them in real GRUB with the command `vbeinfo'
#GRUB_GFXMODE=640x480

# Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux
#GRUB_DISABLE_LINUX_UUID=true

# Uncomment to disable generation of recovery mode menu entries
#GRUB_DISABLE_RECOVERY="true"

# Uncomment to get a beep at grub start
#GRUB_INIT_TUNE="480 440 



Végül az MX Linux grub fájl:

# If you change this file, run 'update-grub' afterwards to update
# /boot/grub/grub.cfg.
# For full documentation of the options in this file, see:
#   info -f grub -n 'Simple configuration'

GRUB_DEFAULT="0"
GRUB_TIMEOUT="60"
GRUB_DISTRIBUTOR="$(unset PRETTY_NAME; (. /etc/lsb-release; echo ${PRETTY_NAME:?}) 2>/dev/null || echo Debian)"
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash apm=power-off"
GRUB_CMDLINE_LINUX=""

# Uncomment to enable BadRAM filtering, modify to suit your needs
# This works with Linux (no patch required) and with any kernel that obtains
# the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...)
#GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"

# Uncomment to disable graphical terminal (grub-pc only)
#GRUB_TERMINAL="console"

# The resolution used on graphical terminal
# note that you can use only modes which your graphic card supports via VBE
# you can see them in real GRUB with the command `vbeinfo'
GRUB_GFXMODE="1024x768"

# Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux
#GRUB_DISABLE_LINUX_UUID="true"

# Uncomment to disable generation of recovery mode menu entries
#GRUB_DISABLE_RECOVERY="true"

# Uncomment to get a beep at grub start
#GRUB_INIT_TUNE="480 440 1"

GRUB_DISABLE_OS_PROBER="false"
#export GRUB_MENU_PICTURE="/usr/share/backgrounds/MXLinux/grub/linen-gradientblu-grub.png"
#export GRUB_MENU_PICTURE="/usr/share/backgrounds/MX18ALPHAWALL.png"

GRUB_THEME="/boot/grub/themes/mx_linux/theme.txt"

#GRUB_DISABLE_LINUX_RECOVERY="true"