Find out what program is using a hotkey

Sorry I can't suggest an alternative to Hotkey Explorer for Windows 8 or 10. It's a godsend on Windows 7.

I can only offer you the most primitive way of handling this problem. First, close all your running programs (including stuff in the system tray), one by one. Make notice of what you close and every time (or every once in a while) test if your program (is it Greenshot?) can now use that hotkey.

If everything is closed but the problem persists, open the Processes tab in the Task Manager (or better yet, download the Sysinternals Process Explorer). Sort processes by user and start killing user (not system) processes one by one. Again, keep checking if the hotkey becomes available. Sooner or later you should find the offending process. In my case, CSRHarmonySkypePlugin.exe (part of CSR Harmony drivers for a CSR Bluetooth 4.0 USB dongle) was grabbing Ctrl+Alt+Up and Down and a few others - with no UI to configure that or turn off!

This kind of problem is extremely annoying. Happy hunting!

A small extension to Gene Pavlovsky's answer: in Sysinternals Process Explorer you can activate Views » Scroll to new processes

Sometimes, the assigned application will be highlighted as soon as you press the hotkey :-)

You can use the tool Spy++ that comes with Visual Studio: https://stackoverflow.com/a/43645062/62838. It will allow you to see what window and process are receiving the WM_HOTKEY window message. If the 32 bit version doesn't work, try the 64 bit version instead.