I liked this script. Good, clean, easy to read. And works overall. I liked the punchline. Always good to have an ending to tie it up nicely.
My one lingering thought was that Louise is a doctor. From a comedy standpoint this is fine, but this reads more like drama/comedy. So I was thinking that Louise would guess that Tim was putting it on. And have that thought in the back of her mind that Tim was just making it up to see her. And Louise would just have a some sort of funny retort to Tim's advances. Just a thought.
Also, I would rewrite the first sentence to a skinny fidgety man sits at a table...
All the best,
Just a point here, but yeah I agree Lousie would probably think there was something up. But, having said that. I went to see my doctor around fifteen times with various feigned illness before I could admit that I had an eating disorder. They never once questioned why or what was going on with me... Just an fyi :)