Those bounds originated from a vector file, I am pretty sure. If they did, get it, add a new field, call it "Dissolve", use the field calculator and calculate a value of 1 in it. Open up the Dissolve tool in arctoolbox and dissolve the bounds using that field. You will then have your area of interest I mentioned several threads ago. Export that to raster will set the inside to 1 and the outside to nodata. From that use that as your analysis mask to assign your input for focal stats to nodata.
If your focal statistics cell size was small and you were using a 3x3 window, you shouldn't see that blending that you are showing. So you are doing something at the focal statistics level, like not specifying a small enough cell size or you didn't preprocess your data prior to doing the focal analysis
... sort of retired...
