"Home is good," Alyssa said. "Food shopping is... probably better. I've got no food left in the apartment." This was a perfectly reasonable, justifiable request. Not because she wanted to spend more time with him to figure out what had happened to her face. No, because her own bed was calling her, and she still had to unpack...
Or... Alyssa mulled over her options - she could ask him right now, point black, in hopes of catching him off his guard. "So when are you going to tell me," what you did to your face "what you were up to while I was gone?"
She'd give him one more chance to come clean on his own before doing her best to shock it out of him.