You shouldn't have to do anything in your pixel shader to get alpha blending to work if everything is setup correctly. If you have alpha blending turned on, the correct blending function and the image is imported properly, then you should be able to just draw the pixels as they are and not worry about it. Because any pixel with an alpha of 0 should get blended out, regardless of the color set on it.
Now, purple is the default clear color for XNA, so, I suspect there is an issue with the order you are doing things. My guess is that your start with a clear render, then draw one pass that processes your effect. And your effect either chooses to draw a pixel from the background or a pixel from the distorted image. The problem is when it chooses to draw a pixel from the distorted image and it has an alpha value less than 1, then it will get blended with what is currently on the render image... which is the default purple. If you go this route, then the proper way would be always draw both a background and a distorted pixel. However, you would have to do the alpha blending yourself. The other issue is that unless your distorted image is always a full screen draw, you will only get a background for the rectangular area where you apply your effect.
What you probably want to do is to draw your entire background to the current render first (and verify it shows up on its own before moving to the next step). And then perform a draw pass applying your distorted effect with alpha blending turned on. In your shader, you wouldn't have to worry about what is in the background at all. You just have to make sure that whatever your effect is doing is not skewing your alpha values in any way that will make the draw fail.
