How do I impress his old world grandmother?

I'm supposed to meet my boyfriend's parents in a week, which is fine, because I'm usually good with parents, but it turns out that after I meet his parents, we're going to have dinner with his grandmother, who came from Greece. He says she is very conservative (not politically conservative, but like old-fashioned conservative). We're both 20, and we've only been dating for about a month (so "boyfriend" is sort of an umbrella term for what we are). But I want to make sure she likes me, because he is pretty close with her, and I don't want her to think I'm slutty. Obviously I'll dress nicely, and not show off too much, but I'm afraid I'll say the wrong thing, or look too ugly for her taste (not sure what she considers pretty.for example I'm very skinny and she might think that looks unhealthy). What do I do?