Maybe he waited in the house for a while for them to get home, and wrote the letter and got everything ready while they were out.
Maybe he was down in the basement with her, he already had the garrotte on her loosely, but he hadn't caused any actual physical pain yet. Possibly when he put the paintbrush handle inside of her, she screamed, and he tightened the garrotte as a reflex to make her be quiet, saw that he pulled it to tight, panicked, hit her in the head, and the grating sound the neighbor heard was him hightailing it out of the basement, through the window maybe? Just my theory.