Product review (3 stars): New Screw piece too small for Existing Thread
New Screw piece too small for Existing Thread.
Would not go on.

This is the right replacement piece per Sears Direct part replacement website.
I had to improvise.
I disassembled the arm by gently squeezing the 3-prong fastener in the center of the part.
Then I snapped the new spray arm onto the old screw piece, using the new, 3-prong fastener that came with the new part.
I made sure all the catch spots were bent back in place.

Screwed right on from there.  Looks like I'm good.
I hate it doesn't fit right out the package...glad I didn't throw away the old parts!!!!