It's not really clear whether you've got a BIOS-mode or an EFI-mode installation of Linux. There's evidence of both, so it's unclear whether the computer is actually booting in EFI mode or in BIOS mode when you boot Linux via GRUB. This is critically important because Windows will boot only in EFI mode from a GPT disk, which you have, and a BIOS version of GRUB cannot boot Windows in EFI mode. Thus, if you're currently booting Linux in BIOS mode, you'll need to change to boot in EFI mode before you do anything else.
To determine your Linux boot mode, look for a directory called /sys/firmware/efi. If it's present, you've booted in EFI mode, and your boot path currently passes through the EFI version of GRUB. If that directory is absent, chances are you've booted in BIOS mode. In that case, you should enter your firmware setup utility and change whatever options you need to change to get the system booting in EFI mode. Unfortunately, I can't be more precise about this because firmware user interfaces vary a lot on this score. Note that you'll probably have to disable Secure Boot (which should be a firmware option) to get this to work. Also, when you change boot modes, you may find that the computer will boot Windows without giving you an option to boot Linux or that it won't boot at all. If that happens, you should report back with details of what happened.
Assuming that you're currently booting Linux in EFI mode or that you can get the computer to do this, you have several choices about how to proceed. The two that are easiest are:
- Type "sudo update-grub". This should trigger GRUB's setup script to detect Windows and add it to the boot menu. Sometimes this doesn't work as expected, though. You could then add a Windows entry to /etc/grub.d/40_custom and try again. Unfortunately, there are a lot of recommended entries out there on the Internet, and what works for one installation does not work for another one, so I've given up on recommending specific entries. Feel free to look up some possible entries and experiment if you want to go this route, though.
- Download and install my rEFInd boot manager. Installing the Debian package in Mint is the easiest way to do this, and installing it from an EFI-booted Linux will do the right thing most of the time. Sometimes this isn't sufficient, though, usually because of a buggy firmware; when this is the case, rEFInd won't appear when you reboot and you'll need to take additional steps. Post back with details of what happened if this occurs to you.
Note that you need only do one
of these two things; however, if one doesn't work, you can try the other one instead.