When you export the Pastel_bg.wix to a gif or png are you using 256 color with Transparency? This creates a sharp file on my system. With the simple colors for the background you can select the 16 color option with good results.

Before exporting to a raster format, position the group that is the Pastel_bg.wix objects so it is on even pixel X and Y positions within Web Designer. This reduces the amount of antialiasing needed and makes the result more sharp.

Xara works at a millipixel level internally so it is possible to have objects located on fractional pixel coordinates.