How can I change the boot screen to show our own logo instead?

You may change the boot image if you wish - we use the usual Plymouth boot splash system used by most mainstream Linux distributions, and have not gone out of our way to obfuscate this in any way - but it is not in our commercial interest to provide you with any assistance in substituting your own branding.

If you find our boot screen too obtrusive, you can SSH to your TLXOS device as root, then run the following commands to turn it off:

mount -o remount,rw /boot
for CFGFILE in config.txt syslinux/syslinux.cfg EFI/BOOT/syslinux.cfg; do
    [ -e $CFGFILE ] && sed -i -e 's/\<splash/nosplash loglevel=0/' /boot/$CFGFILE
done
mount -o remount,ro /boot

You can customize the post-bootup background image using TMS' File->Install File option with File Type set to Wallpaper Image, or the equivalent option in Tlxconfig's Misc tab.