They did commit what they'll reluctantly admit were mass killings of Armenians (what the rest of the world correctly recognizes as genocide) in the aftermath of World War I.
During the Ottoman era, they did occupy Greece and were, like virtually every occupying force, remarkably brutal. This got a lot of attention in the West because they were oppressing Europeans and Christians (instead of Asians and Muslims).
But here's a story about them. During the Irish genocide by famine (when a country exports food during a famine and the occupying foreign land owners raise rents during a period of starvation, that's genocide, whether the original cause was natural or not), the then Sultan of Turkey, Abdul Majid Khan, offered to send food and 10,000 pounds sterling. England refused to allow this.
Why? Why would it refuse the kind of aid that would have saved several thousand lives?
Queen Victoria gave only two thousand pounds and a gift greater than that would make her look ungenerous.
The Sultan insisted on giving something and finally they bargained him down to one thousand pounds. He also send three ships worth of food, but kept it quiet.