Amycus did not kill Greta Gamp. I did. She was a horrid bitch with a foul mouth, and nowhere near good enough to become a Carrow. It was an accident, I will admit, but one I regret if only because my brother is taking the fall for me. He wouldn't want me doing this, but I can't let him go to Azkaban, or worse, because I lost control. I will turn myself in willingly, but you must first guarantee my brother's safe release. He was only trying to protect me, and does not deserve to be punished for it.
If you don't believe me, here is the truth. The bitch came over and they had their date. When she came back downstairs, to the room I was reading in, she talked about how she had him right where she wanted him, how she wouldn't be surprised if he proposed within a few weeks; I would be kicked out of my home and she would have our money to spend on whatever she wanted. I lost control and hexed her, killing her nearly instantly, but leaving a lot of blood behind. I then rolled the body up in the carpet and had our house elf dispose of her somewhere outside the country. Amycus didn't know what happened until I told him later that night.
If you do not believe me, test my wand, and you will find the killing hex was issued from it. I will trade my life for my brother's, but only once his freedom is secured. I will be at our manor tonight at exactly eleven o'clock, if Amycus is freed. Bring him with you when you come to arrest me. If he isn't there, I don't show.