I am struggling to come up with a thesis statement for "The Garden Party." Can you help me out?

I would strongly suggest that you begin by taking a look at the themes section of the enotes study guide to this brilliant short story. I have included the link below. This will help you identify the main themes of the story. The easiest way to come up with a thesis statement is to pick a theme and use that as the basis for forming your thesis statement. For example, one of the principal themes of this short story is class and Laura's awareness of it. Note the comments that she makes at the beginning where she pretends to be immune to class consciousness:

It's all the fault, she decided, as the tall fellow drew something on teh back of an envelope, something that was to be looped up or left to hang, of these absurd class distinctions. Well, for her part, she didn't feel them. Not a bit, not an atom...

However, when she tries to have the garden party cancelled because of the death of Mr. Scott, a working class man from a nearby cottage, she finds out that her family do not share her views, and she herself comes to think they were rather silly. It is only when she goes to see the body of Mr. Scott that she is forced to realise the way in which his death and peace represents a kind of comment upon the frivolous nature of garden parties and her life. A thesis statement that you could use therefore might be:

The development of the character of Laura in "The Garden Party" allows Mansfield to comment upon class and the barriers that divide different people in society.

This thesis statement will allow you to focus on Laura and how she changes throughout the story, and what Mansfield achieves through that change. Hope these ideas help. Good luck!