That's a bad particle shape image. Some of the older shape images didn't fade out near the edges. To fix it, you have to fix the shape. Here's how I typically do it:
1) open the emitter properties dialog
2) select the "bad" shape on the "change shape" page, and click the "export" button. Save the image as PNG or TGA.
3) Open the image in your favorite paint app, and adjust the contrast a little, darken the lows, or whatever to darken the image a little around the edges.
4) Take the eyedropper tool and run it around the edges of the image, making sure that the pixels go to RGB 0,0,0. If they even go to 1,1,1 they will form those sharp edges when enough of them are drawn on top of each other.
5) Save the image, reimport into particleIllusion
6) I suggest renaming the "bad" shape with "_bad", so you don't get them mixed up.
If you just want to replace the bad shape in this one emitter only (the safer choice) just "make current" for the particle type.
If you want to replace that bad shape with the new one in ALL of the emitters in the current library, do the following:
7) Drag the new shape so it's right *above* the "bad" image in the list
8) Delete the "bad" shape from the list. All particle types that use the "bad" shape will now use the shape above it in the list -- the new "good" shape.