The bootinfoscript shows Gru2 installed to the mbr and pointing to sda9 where you have one of your Peppermint installs. It has an entry for Peppermint. Your sda7 also has a grub.cfg file which does NOT show an entry for Peppermint but does show memtest and windows entries. I don't know why you would be seeing that. You could try reinstalling Grub2 pointing to sda9 from the Peppermint CD. If you boot it up and open a terminal type the following commands consecutively, hit the Enter key after each command:
sudo mkdir /mnt/sda9
sudo mount -t ext4 /dev/sda9 /mnt/sda9
sudo grub-install --root-directory=/mnt/sda9 /dev/sda
Have you made any changes since you posted the bootinfoscript?