Should she tell Strange to give her the scarf back? Nah, it was a cheap scrap of fabric. She'll just let him make a goofy face over being asked to get a drink with her without comment.

"Mm, I don't really know that many places around here. Leave it to me and I'll pick somewhere close to the place I got a room." Cheap and close to her bed. Shura has her priorities, and if Strange doesn't have any other suggestions, that's just where she'll take him.